How to find f(x) - GRE Quantitative Reasoning
Card 0 of 272
A function f(x) = –1 for all values of x. Another function g(x) = 3_x_ for all values of x. What is g(f(x)) when x = 4?
A function f(x) = –1 for all values of x. Another function g(x) = 3_x_ for all values of x. What is g(f(x)) when x = 4?
We work from the inside out, so we start with the function f(x). f(4) = –1. Then we plug that value into g(x), so g(f(x)) = 3 * (–1) = –3.
We work from the inside out, so we start with the function f(x). f(4) = –1. Then we plug that value into g(x), so g(f(x)) = 3 * (–1) = –3.
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What is f(–3) if f(x) = _x_2 + 5?
What is f(–3) if f(x) = _x_2 + 5?
f(–3) = (–3)2 + 5 = 9 + 5 = 14
f(–3) = (–3)2 + 5 = 9 + 5 = 14
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For all values of x, f(x) = 7_x_2 – 3, and for all values of y, g(y) = 2_y_ + 9. What is g(f(x))?
For all values of x, f(x) = 7_x_2 – 3, and for all values of y, g(y) = 2_y_ + 9. What is g(f(x))?
The inner function f(x) is like our y-value that we plug into g(y).
g(f(x)) = 2(7_x_2 – 3) + 9 = 14_x_2 – 6 + 9 = 14_x_2 + 3.
The inner function f(x) is like our y-value that we plug into g(y).
g(f(x)) = 2(7_x_2 – 3) + 9 = 14_x_2 – 6 + 9 = 14_x_2 + 3.
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g(x) = 4x – 3
h(x) = .25πx + 5
If f(x)=g(h(x)). What is f(1)?
g(x) = 4x – 3
h(x) = .25πx + 5
If f(x)=g(h(x)). What is f(1)?
First, input the function of h into g. So f(x) = 4(.25πx + 5) – 3, then simplify this expression f(x) = πx + 20 – 3 (leave in terms of πsince our answers are in terms of π). Then plug in 1 for x to get π+ 17.
First, input the function of h into g. So f(x) = 4(.25πx + 5) – 3, then simplify this expression f(x) = πx + 20 – 3 (leave in terms of πsince our answers are in terms of π). Then plug in 1 for x to get π+ 17.
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If a(x) = 2x3 + x, and b(x) = –2x, what is a(b(2))?
If a(x) = 2x3 + x, and b(x) = –2x, what is a(b(2))?
When functions are set up within other functions like in this problem, the function closest to the given variable is performed first. The value obtained from this function is then plugged in as the variable in the outside function. Since b(x) = –2x, and x = 2, the value we obtain from b(x) is –4. We then plug this value in for x in the a(x) function. So a(x) then becomes 2(–43) + (–4), which equals –132.
When functions are set up within other functions like in this problem, the function closest to the given variable is performed first. The value obtained from this function is then plugged in as the variable in the outside function. Since b(x) = –2x, and x = 2, the value we obtain from b(x) is –4. We then plug this value in for x in the a(x) function. So a(x) then becomes 2(–43) + (–4), which equals –132.
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Let F(x) = _x_3 + 2_x_2 – 3 and G(x) = x + 5. Find F(G(x))
Let F(x) = _x_3 + 2_x_2 – 3 and G(x) = x + 5. Find F(G(x))
F(G(x)) is a composite function where the expression G(x) is substituted in for x in F(x)
F(G(x)) = (x + 5)3 + 2(x + 5)2 – 3 = x_3 + 17_x_2 + 95_x + 172
G(F(x)) = _x_3 + _x_2 + 2
F(x) – G(x) = _x_3 + 2_x_2 – x – 8
F(x) + G(x) = _x_3 + 2_x_2 + x + 2
F(G(x)) is a composite function where the expression G(x) is substituted in for x in F(x)
F(G(x)) = (x + 5)3 + 2(x + 5)2 – 3 = x_3 + 17_x_2 + 95_x + 172
G(F(x)) = _x_3 + _x_2 + 2
F(x) – G(x) = _x_3 + 2_x_2 – x – 8
F(x) + G(x) = _x_3 + 2_x_2 + x + 2
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What is the value of xy_2(xy – 3_xy) given that x = –3 and y = 7?
What is the value of xy_2(xy – 3_xy) given that x = –3 and y = 7?
Evaluating yields –6174.
–147(–21 + 63) =
–147 * 42 = –6174
Evaluating yields –6174.
–147(–21 + 63) =
–147 * 42 = –6174
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Given the functions f(x) = 2_x_ + 4 and g(x) = 3_x_ – 6, what is f(g(x)) when x = 6?
Given the functions f(x) = 2_x_ + 4 and g(x) = 3_x_ – 6, what is f(g(x)) when x = 6?
We need to work from the inside to the outside, so g(6) = 3(6) – 6 = 12.
Then f(g(6)) = 2(12) + 4 = 28.
We need to work from the inside to the outside, so g(6) = 3(6) – 6 = 12.
Then f(g(6)) = 2(12) + 4 = 28.
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If f(x)=3x and g(x)=2x+2, what is the value of f(g(x)) when x=3?
If f(x)=3x and g(x)=2x+2, what is the value of f(g(x)) when x=3?
With composition of functions (as with the order of operations) we perform what is inside of the parentheses first. So, g(3)=2(3)+2=8 and then f(8)=24.
With composition of functions (as with the order of operations) we perform what is inside of the parentheses first. So, g(3)=2(3)+2=8 and then f(8)=24.
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The function
is defined as
. What is
?
The function is defined as
. What is
?
Substitute -1 for
in the given function.




If you didn’t remember the negative sign, you will have calculated 36. If you remembered the negative sign at the very last step, you will have calculated -36; however, if you did not remember that
is 1, then you will have calculated 18.
Substitute -1 for in the given function.
If you didn’t remember the negative sign, you will have calculated 36. If you remembered the negative sign at the very last step, you will have calculated -36; however, if you did not remember that is 1, then you will have calculated 18.
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What is the value of the function f(x) = 6x2 + 16x – 6 when x = –3?
What is the value of the function f(x) = 6x2 + 16x – 6 when x = –3?
There are two ways to do this problem. The first way just involves plugging in –3 for x and solving 6〖(–3)〗2 + 16(–3) – 6, which equals 54 – 48 – 6 = 0. The second way involves factoring the polynomial to (6x – 2)(x + 3) and then plugging in –3 for x. The second way quickly shows that the answer is 0 due to multiplying by (–3 + 3).
There are two ways to do this problem. The first way just involves plugging in –3 for x and solving 6〖(–3)〗2 + 16(–3) – 6, which equals 54 – 48 – 6 = 0. The second way involves factoring the polynomial to (6x – 2)(x + 3) and then plugging in –3 for x. The second way quickly shows that the answer is 0 due to multiplying by (–3 + 3).
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If
and
, what is
?
If and
, what is
?
Plug g(x) into f(x) as if it is just a variable. This gives f(g(x)) = 3(x2 – 12) + 7.
Distribute the 3: 3x2 – 36 + 7 = 3x2 – 29
Plug g(x) into f(x) as if it is just a variable. This gives f(g(x)) = 3(x2 – 12) + 7.
Distribute the 3: 3x2 – 36 + 7 = 3x2 – 29
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If the function
is created by shifting
up four units and then reflecting it across the x-axis, which of the following represents
in terms of
?
If the function is created by shifting
up four units and then reflecting it across the x-axis, which of the following represents
in terms of
?
We can take each of the listed transformations of
one at a time. If
is to be shifted up by four units, increase every value of
by 4.

Next, take this equation and reflect it across the x-axis. If we reflect a function across the x-axis, then all of its values will be multiplied by negative one. So,
can be written in the following way:

Lastly, distribute the negative sign to arrive at the final answer.

We can take each of the listed transformations of one at a time. If
is to be shifted up by four units, increase every value of
by 4.
Next, take this equation and reflect it across the x-axis. If we reflect a function across the x-axis, then all of its values will be multiplied by negative one. So, can be written in the following way:
Lastly, distribute the negative sign to arrive at the final answer.
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If 7y = 4x - 12, then x =
If 7y = 4x - 12, then x =
Adding 12 to both sides and dividing by 4 yields (7y+12)/4.
Adding 12 to both sides and dividing by 4 yields (7y+12)/4.
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Which of the statements describes the solution set for **–**7(x + 3) = **–**7x + 20 ?
Which of the statements describes the solution set for **–**7(x + 3) = **–**7x + 20 ?
By distribution we obtain **–**7x – 21 = – 7x + 20. This equation is never possibly true.
By distribution we obtain **–**7x – 21 = – 7x + 20. This equation is never possibly true.
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A function F is defined as follows:
for x2 > 1, F(x) = 4x2 + 2x – 2
for x2 < 1, F(x) = 4x2 – 2x + 2
What is the value of F(1/2)?
A function F is defined as follows:
for x2 > 1, F(x) = 4x2 + 2x – 2
for x2 < 1, F(x) = 4x2 – 2x + 2
What is the value of F(1/2)?
For F(1/2), x2=1/4, which is less than 1, so we use the bottom equation to solve. This gives F(1/2)= 4(1/2)2 – 2(1/2) + 2 = 1 – 1 + 2 = 2
For F(1/2), x2=1/4, which is less than 1, so we use the bottom equation to solve. This gives F(1/2)= 4(1/2)2 – 2(1/2) + 2 = 1 – 1 + 2 = 2
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For which value of
are the following two functions equal?


For which value of are the following two functions equal?
It is important to follow the order of operations for this equation and find a solution that satisfies both F(x) and G(x).
Recall the order of operations is PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
The correct answer is 4 because
F(x) = 2_x_ + 3_x_ + (9_x_/3) = 2(4) + 34 + ((9 * 4)/3) = 101, and
G(x) = (((24 + 44)/2) - 4 * 4) – 5(4) + 1 = 101.
It is important to follow the order of operations for this equation and find a solution that satisfies both F(x) and G(x).
Recall the order of operations is PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
The correct answer is 4 because
F(x) = 2_x_ + 3_x_ + (9_x_/3) = 2(4) + 34 + ((9 * 4)/3) = 101, and
G(x) = (((24 + 44)/2) - 4 * 4) – 5(4) + 1 = 101.
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What is
?
What is ?
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If F(x) = 2x2 + 3 and G(x) = x – 3, what is F(G(x))?
If F(x) = 2x2 + 3 and G(x) = x – 3, what is F(G(x))?
A composite function substitutes one function into another function and then simplifies the resulting expression. F(G(x)) means the G(x) gets put into F(x).
F(G(x)) = 2(x – 3)2 + 3 = 2(x2 – 6x +9) + 3 = 2x2 – 12x + 18 + 3 = 2x2 – 12x + 21
G(F(x)) = (2x2 +3) – 3 = 2x2
A composite function substitutes one function into another function and then simplifies the resulting expression. F(G(x)) means the G(x) gets put into F(x).
F(G(x)) = 2(x – 3)2 + 3 = 2(x2 – 6x +9) + 3 = 2x2 – 12x + 18 + 3 = 2x2 – 12x + 21
G(F(x)) = (2x2 +3) – 3 = 2x2
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Find 

Find
Simply plug 6 into the equation and don't forget the absolute value at the end.

absolute value = 67
Simply plug 6 into the equation and don't forget the absolute value at the end.
absolute value = 67
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