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PSAT Math : How to find f(x)

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Example Questions

Example Question #71 : How To Find F(X)

If is an odd integer, and is an even integer, which of the following must be even?

Possible Answers:

3a+3b

4a+3b

ab+1

2b-3a

3a-b

Correct answer:

4a+3b

Explanation:

Solve this problem using picked numbers. Choose an odd number to represent and an even number to represent . In this case, we have chosen 3 to represent and 2 to represent .

Substitute into each equation to find the correct answer:

4a+3b = 4(3)+3(2)=12+6=18

This number is even, and likely the answer we are looking for. Just in case, quickly check the other answers to make sure no others come out even.

3a+3b = 3(3)+3(2)=9+6=15

This expression gives an odd answer and must be incorrect.

3a-b = 3(3)-2=9-2=7

This expression gives an odd answer and must be incorrect.

2b-3a = 2(2)-3(3)=4-9=-5

This expression gives an odd answer and must be incorrect.

ab+1 = 2*3+1=6+1=7

This expression gives an odd answer and must be incorrect.

Only the first answer is even. The answer is 4a+3b .

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Example Question #72 : Algebraic Functions

If $f\left ( x\right ) = x^{2}+2\left(\frac{x}{4}\right)+\sqrt{x}$

What is f(4) ?

Possible Answers:

$20+\sqrt{4}$

200

Correct answer:

Explanation:

To find f(4), input a 4 in every place you see an x in the equation. That gives you

$f\left ( 4\right ) = 4^{2}+2\left(\frac{4}{4}\right)+\sqrt{4}$

When you simplify this expression, you get

$f\left ( 4\right ) = 16+2(1)+2$

When you add together each part, you get

$f\left ( 4\right ) = 20$

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Example Question #15 : Algebraic Functions

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 #14 : Algebraic Functions

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 #15 : Algebraic Functions

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

–3

–12

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 #17 : Algebraic Functions

What is f(–3) if f(x) = x² + 5?

Possible Answers:

–4

–14

Correct answer:

Explanation:

f(–3) = (–3)² + 5 = 9 + 5 = 14

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Example Question #21 : Algebraic Functions

For all values of x, f(x) = 7x² – 3, and for all values of y, g(y) = 2y + 9. What is g(f(x))?

Possible Answers:

14y² + 3

2x + 9

14x² + 3

7y² – 3

14x² – 3

Correct answer:

14x² + 3

Explanation:

The inner function f(x) is like our y-value that we plug into g(y).

g(f(x)) = 2(7x² – 3) + 9 = 14x² – 6 + 9 = 14x² + 3.

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Example Question #22 : Algebraic Functions

Find f(6)

$f(x)=|x^{2}+4x-127|$

Possible Answers:

Correct answer:

Explanation:

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

=36+24-127=-67

absolute value = 67

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Example Question #41 : Algebraic Functions

An outpost has the supplies to last 2 people for 14 days. How many days will the supplies last for 7 people?

Possible Answers:

$\dpi{100} \small 9$

$\dpi{100} \small 4$

$\dpi{100} \small 7$

$\dpi{100} \small 5$

$\dpi{100} \small 10$

Correct answer:

$\dpi{100} \small 4$

Explanation:

Supplies are used at the rate of $\dpi{100} \small \frac{Supplies}{Days\times People}$ .

Since the total amount of supplies is the same in either case, $\dpi{100} \small \frac{1}{14\times 2}=\frac{1}{7\times \ (\&hash;\ of\ days)}$ .

Solve for days to find that the supplies will last for 4 days.

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Example Question #23 : Algebraic Functions

Worker $\dpi{100} \small A$ can make a trinket in 4 hours, Worker $\dpi{100} \small B$ can make a trinket in 2 hours. When they work together, how long will it take them to make a trinket?

Possible Answers:

$\dpi{100} \small \frac{1}{2}\ hour$

$\dpi{100} \small \ 1 \frac{1}{3}\ hours$

$\dpi{100} \small 6\ hours$

$\dpi{100} \small \ 1 \frac{1}{2}\ hours$

$\dpi{100} \small 3\ hours$

Correct answer:

$\dpi{100} \small \ 1 \frac{1}{3}\ hours$

Explanation:

The rates are what needs to be added. Rate $\dpi{100} \small A$ is $\dpi{100} \small \frac{1}{4}$ , or one trinket every 4 hours. Rate $\dpi{100} \small B$ is $\dpi{100} \small \frac{1}{2}$ , one per two hours.

$\dpi{100} \small \frac{1}{4}+ \frac{1}{2}=\frac{3}{4}$ , their combined rate in trinkets per hour.

Now invert the equation to get back to hours per trinket, which is what the question asks for: $\dpi{100} \small \frac{4}{3}\ or \ 1 \frac{1}{3}$

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PSAT Math : How to find f(x)

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #71 : How To Find F(X)

Example Question #72 : Algebraic Functions

Example Question #15 : Algebraic Functions

Example Question #14 : Algebraic Functions

Example Question #15 : Algebraic Functions

Example Question #17 : Algebraic Functions

Example Question #21 : Algebraic Functions

Example Question #22 : Algebraic Functions

Example Question #41 : Algebraic Functions

Example Question #23 : Algebraic Functions

All PSAT Math Resources

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