SAT Math : Algebraic Functions
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Example Questions
Example Question #1001 : Algebra
Jamie is three times her little brother's age, and her little brother is two years younger than his older brother. Collectively, the three of them are 27 years old. How old is Jamie?
None of the available answers
The algebraic expression for 
Jamie's youngest brother is five, the next oldest brother is seven, and Jamie is 15.
Example Question #81 : Algebraic Functions
Consider the function defined as follows:
Find:
The notation used above can be confusing. Let:
We can now find the answer by substituting the appropriate values into the equation:
Therefore:
Finally:
Example Question #2781 : Sat Mathematics
Solve for 
To solve for 
The answer of 
Example Question #11 : Algebraic Functions
If f(x)=3x and g(x)=2x+2, what is the value of f(g(x)) when x=3?
18
22
24
20
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.
Example Question #1 : How To Find F(X)
g(x) = 4x – 3
h(x) = .25πx + 5
If f(x)=g(h(x)). What is f(1)?
19π – 3
π + 17
13π + 3
4
42
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 π since our answers are in terms of π). Then plug in 1 for x to get π + 17.
Example Question #1 : How To Find F(X)
If 7y = 4x - 12, then x =
Adding 12 to both sides and dividing by 4 yields (7y+12)/4.
Example Question #1 : How To Find F(X)
If F(x) = 2x2 + 3 and G(x) = x – 3, what is F(G(x))?
6x2 – 12x
2x2
6x2 + 5x
2x2 – 12x +21
2x2 + 12x +18
2x2 – 12x +21
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
Example Question #1 : Algebraic Functions
If a(x) = 2x3 + x, and b(x) = –2x, what is a(b(2))?
503
–132
132
–503
128
–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.
Example Question #2671 : Act Math
Let F(x) = x3 + 2x2 – 3 and G(x) = x + 5. Find F(G(x))
x3 + 2x2 – x – 8
x3 + 2x2 + x + 2
x3 + x2 + x + 8
x3 + x2 + 2
x3 + 17x2 + 95x + 172
x3 + 17x2 + 95x + 172
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 = x3 + 17x2 + 95x + 172
G(F(x)) = x3 + x2 + 2
F(x) – G(x) = x3 + 2x2 – x – 8
F(x) + G(x) = x3 + 2x2 + x + 2
Example Question #8 : How To Find F(X)
What is the value of xy2(xy – 3xy) given that x = –3 and y = 7?
3565
–2881
2881
–6174
–6174
Evaluating yields –6174.
–147(–21 + 63) =
–147 * 42 = –6174
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