GRE Math : Algebra

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Example Questions

Example Question #2795 : Sat Mathematics

If $\small f(x) = 4x^{2}+3x+2$ $\displaystyle \small f(x) = 4x^{2}+3x+2$ and $\small g(x) = x+7$ $\displaystyle \small g(x) = x+7$, what is $\small f(g(x))$ $\displaystyle \small f(g(x))$?

Possible Answers:

$\small 4x^{2}+17x+219$ $\displaystyle \small 4x^{2}+17x+219$

$\small 4x^{2}+3x+219$ $\displaystyle \small 4x^{2}+3x+219$

$\small 4x^{2}+59x+219$ $\displaystyle \small 4x^{2}+59x+219$

$\small 4x^{2}+17x+72$ $\displaystyle \small 4x^{2}+17x+72$

$\small 4x^{2}+3x+72$ $\displaystyle \small 4x^{2}+3x+72$

Correct answer:

$\small 4x^{2}+59x+219$ $\displaystyle \small 4x^{2}+59x+219$

Explanation:

$\small 4(x+7)^{2} +3(x+7)+2$ $\displaystyle \small 4(x+7)^{2} +3(x+7)+2$

$\small 4(x^{2} + 14x + 49)+ 3x +21 + 2$ $\displaystyle \small 4(x^{2} + 14x + 49)+ 3x +21 + 2$

$\small 4x^{2}+56x+196+3x+23$ $\displaystyle \small 4x^{2}+56x+196+3x+23$

$\small 4x^{2}+59x+219$ $\displaystyle \small 4x^{2}+59x+219$

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Example Question #2796 : Sat Mathematics

If f(6)=7 $\displaystyle f(6)=7$ and $\displaystyle f(10)=17$, which of the following could represent f(x) $\displaystyle f(x)$?

Possible Answers:

$\displaystyle 2.5x - 8$

$\displaystyle 1.5x - 2$

x + 4 $\displaystyle x + 4$

2x + 5 $\displaystyle 2x + 5$

3x - 1 $\displaystyle 3x - 1$

Correct answer:

$\displaystyle 2.5x - 8$

Explanation:

The number in the parentheses is what goes into the function.

For the function $\displaystyle f(x) = 2.5x - 8$,

$\displaystyle f(6) = 2.5(6) - 8 = 7$ and

$\displaystyle f(10) = 2.5(10) - 8 = 17$

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Example Question #2800 : Sat Mathematics

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)?

Possible Answers:

$\displaystyle 4$

$\displaystyle 0$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{7}{2}$ $\displaystyle \frac{7}{2}$

$\displaystyle 2$

Correct answer:

$\displaystyle 2$

Explanation:

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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Example Question #2801 : Sat Mathematics

Which of the statements describes the solution set for –7(x + 3) = –7x + 20 ?

Possible Answers:

x = –1

All real numbers are solutions.

There are no solutions.

x = 0

Correct answer:

There are no solutions.

Explanation:

By distribution we obtain –7x – 21 = – 7x + 20. This equation is never possibly true.

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Example Question #11 : How To Find F(X)

Will just joined a poetry writing group in town that meets once a week. The number of poems Will has written after a certain number of meetings can be represented by the function $\displaystyle f(p) = 2p+6$, where $\displaystyle p$ represents the number of meetings Will has attended. Using this function, how many poems has Will written after 7 classes?

Possible Answers:

$\displaystyle 20$

$\displaystyle 21$

$\displaystyle 15$

$\displaystyle 19$

$\displaystyle 14$

Correct answer:

$\displaystyle 20$

Explanation:

For this function, simply plug 7 in for $\displaystyle p$ and solve:

$\displaystyle f(p)=2p+6=2(7)+6=20$

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Example Question #62 : Algebraic Functions

If $f(x)=x^{2}+3$ $\displaystyle f(x)=x^{2}+3$, then $f(x+h)=$ $\displaystyle f(x+h)=$ ?

Possible Answers:

$x^{2}+3+h$ $\displaystyle x^{2}+3+h$

$x^{2}+h^{2}+3$ $\displaystyle x^{2}+h^{2}+3$

$x^{2}+2xh+h^{2}$ $\displaystyle x^{2}+2xh+h^{2}$

$x^{2}+2xh+h^{2}+3$ $\displaystyle x^{2}+2xh+h^{2}+3$

$x^{2}+h^{2}$ $\displaystyle x^{2}+h^{2}$

Correct answer:

$x^{2}+2xh+h^{2}+3$ $\displaystyle x^{2}+2xh+h^{2}+3$

Explanation:

To find $f(x+h)$ $\displaystyle f(x+h)$ when $f(x)=x^{2}+3$ $\displaystyle f(x)=x^{2}+3$, we substitute $(x+h)$ $\displaystyle (x+h)$ for $x$ $\displaystyle x$ in $f(x)$ $\displaystyle f(x)$.

Thus, $f(x+h)=(x+h)^{2}+3$ $\displaystyle f(x+h)=(x+h)^{2}+3$.

We expand $(x+h)^{2}$ $\displaystyle (x+h)^{2}$ to $x^{2}+xh+xh+h^{2}$ $\displaystyle x^{2}+xh+xh+h^{2}$.

We can combine like terms to get $x^{2}+2xh+h^{2}$ $\displaystyle x^{2}+2xh+h^{2}$.

We add 3 to this result to get our final answer.

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Example Question #12 : How To Find F(X)

What is the value of the function f(x) = 6x²+ 16x – 6 when x = –3?

Possible Answers:

–108

–12

Correct answer:

Explanation:

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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Example Question #13 : How To Find F(X)

Given the functions f(x) = 2x + 4 and g(x) = 3x – 6, what is f(g(x)) when x = 6?

Possible Answers:

144

192

Correct answer:

Explanation:

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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Example Question #1041 : Algebra

A function f(x) = –1 for all values of x. Another function g(x) = 3x for all values of x. What is g(f(x)) when x = 4?

Possible Answers:

–1

–12

–3

Correct answer:

–3

Explanation:

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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Example Question #1042 : Algebra

What is f(–3) if f(x) = x² + 5?

Possible Answers:

–14

–4

Correct answer:

Explanation:

f(–3) = (–3)² + 5 = 9 + 5 = 14

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GRE Math : Algebra

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #2795 : Sat Mathematics

Example Question #2796 : Sat Mathematics

Example Question #2800 : Sat Mathematics

Example Question #2801 : Sat Mathematics

Example Question #11 : How To Find F(X)

Example Question #62 : Algebraic Functions

Example Question #12 : How To Find F(X)

Example Question #13 : How To Find F(X)

Example Question #1041 : Algebra

Example Question #1042 : Algebra

All GRE Math Resources

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