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PSAT Math : PSAT Mathematics

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Example Questions

Example Question #961 : Psat Mathematics

if $f(x) = x^{2} + x - 2$ and $g(x) = x - 3$ , solve $f(g(x))$ .

Possible Answers:

$f(g(x)) = x^{2} + 1$

$f(g(x)) = x^{2} - 3$

$f(g(x)) = x^{2} + 2x - 5$

$f(g(x)) = x^{2} - 5x + 4$

$f(g(x)) = x^{2} + x - 3$

Correct answer:

$f(g(x)) = x^{2} - 5x + 4$

Explanation:

We are solving for a composite function by substituting $g(x)$ into $f(x)$ to get: $f(g(x)) = (x - 3)^{2} + (x - 3) - 2$ before simplification.

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Example Question #78 : Algebraic Functions

If $f(x)=2x^2-5$ where is an integer, which of the following could be a value of f(x) ?

II.

III.

Possible Answers:

II only

I and III only

II and III only

I only

I, II and III

Correct answer:

II and III only

Explanation:

Choice I is incorrect because to equal 0, $x^2=5$ , and since is an integer, this cannot be true.

Choice II is correct because f(x)=3 when x=2 or x=-2 .

Choice III is correct because f(x)=-3 when x=1 or x=-1 .

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Example Question #272 : New Sat

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?

Possible Answers:

None of the available answers

Correct answer:

Explanation:

The algebraic expression for being Jamie's youngest brother's age is:

3x+x+(x+2)=27

5x+2=27

5x=25

x=5

Jamie's youngest brother is five, the next oldest brother is seven, and Jamie is 15.

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Example Question #962 : Psat Mathematics

Consider the function defined as follows:

$a \Delta b = (a-b)^3 +b$

Find:

$(3 \Delta 5) \times (2 \Delta 0)$

Possible Answers:

Correct answer:

Explanation:

The notation used above can be confusing. Let:

$a \Delta b = f(a,b)$

We can now find the answer by substituting the appropriate values into the equation:

$a \Delta b= f(a,b) = (a-b)^3 +b$

Therefore:

$3 \Delta 5 = f(3,5) = (3-5)^3 + 5 = (-2)^3 + 5 = -3$

$2 \Delta 0 = f(2,0) = (2-0)^3 + 0 = 8$

Finally:

$(3 \Delta 5) \times (2 \Delta 0) = (-3) \times 8 = -24$

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Example Question #963 : Psat Mathematics

Solve for f(2) .

f(x)= 2x-22

Possible Answers:

$\frac{1}{18}$

$-\frac{1}{11}$

Correct answer:

Explanation:

To solve for f(2) , we actually have to solve for f(x) , when x=2 . We simply replace any $\small x$ with a $\small 2$ .

f(x) = 2x - 22

f(2)= 2(2)-22

f(2)= 4-22

f(2)= -18

The answer of f(x) when x=2 is .

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Example Question #1 : Algebraic Functions

If f(x)=3x and g(x)=2x+2, what is the value of f(g(x)) when x=3?

Possible Answers:

Correct answer:

Explanation:

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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Example Question #2 : Algebraic Functions

g(x) = 4x – 3

h(x) = .25πx + 5

If f(x)=g(h(x)). What is f(1)?

Possible Answers:

π + 17

13π + 3

19π – 3

Correct answer:

π + 17

Explanation:

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.

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Example Question #411 : Algebra

If 7y = 4x - 12, then x =

Possible Answers:

(7y-12)/4

(7y+3)/12

(7y+12)/3

(7y+12)/4

Correct answer: (7y+12)/4

Explanation:

Adding 12 to both sides and dividing by 4 yields (7y+12)/4.

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Example Question #3 : Algebraic Functions

f(x) = x^2 + 32x -12

What is f(4) ?

Possible Answers:

128

156

132

130

144

Correct answer:

132

Explanation:

f(x) = x^2 + 32x -12

f(4) = 4^2 + 32(4) -12

= 16 + 128 -12

= 132

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Example Question #4 : Algebraic Functions

If F(x) = 2x² + 3 and G(x) = x – 3, what is F(G(x))?

Possible Answers:

6x² – 12x

2x²

2x² – 12x +21

2x² + 12x +18

6x² + 5x

Correct answer:

2x² – 12x +21

Explanation:

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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PSAT Math : PSAT Mathematics

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #961 : Psat Mathematics

Example Question #78 : Algebraic Functions

Example Question #272 : New Sat

Example Question #962 : Psat Mathematics

Example Question #963 : Psat Mathematics

Example Question #1 : Algebraic Functions

Example Question #2 : Algebraic Functions

Example Question #411 : Algebra

Example Question #3 : Algebraic Functions

Example Question #4 : Algebraic Functions

All PSAT Math Resources

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