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SAT Math : SAT Mathematics

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Example Questions

Example Question #1074 : Algebra

f(x)=3x^2 -12x and f(3t)=36 .

If is a positive integer, what is the value of ?

Possible Answers:

Correct answer:

Explanation:

f(x)=3x^2 -12x

f(3t)=36

First, substitute 3t for x and set the equation equal to 36

3(3t)^2 -12(3t)=36

3(9t^2) -36t=36

Then manipulate the equation so the equation equals 0.

27t^2 -36t-36=0

Factor out 9.

9(3t^2 -4t-4)=0

Divide by 9

$\frac{9(3t^2 -4t-4)}{9}=\frac{0}{9}$

3t^2 -4t-4=0

Factor the equation and solve

(3t+2)(t-2)=0

$t-2=0\: and\: 3t+2=0$

$t=2\: and\: t=-\frac{2}{3}$

Because t is a positive integer, the answer is t=2.

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Example Question #1075 : Algebra

If f(x)=2x+4 , what is the value of f(2) ?

Possible Answers:

Correct answer:

Explanation:

Whenever there is a function, all you need to do is plug in the value into the function.

f(x)=2x+4

f(2)=2(2)+4

f(2)=4+4

f(2)=8

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Example Question #1071 : Algebra

If f(x)=6x-12 , what is -2f(3)+2 ?

Possible Answers:

Correct answer:

Explanation:

Whenever there is a function, all you need to do is plug in the value into the function.

f(x)=6x-12

-2f(3)+2=-2(6(3)-12)+2

=-2(18-12)+2

=-2*6+2

=-12+2

=-10

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Example Question #142 : Algebraic Functions

If f(x)=x^2-3 , then what is 4f(x)+1 for all real values of ?

Possible Answers:

4x^2+1

4x^2+3

4x^2-11

4x^2-2

4x^2-12

Correct answer:

4x^2-11

Explanation:

Whenever there is a function, all you need to do is plug in the value into the function.

f(x)=x^2-3

4f(x)+1=4(x^2-3)+1

=4x^2-12+1

=4x^2-11

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Example Question #141 : Algebraic Functions

If f(x)=x^2+2 , then what is f(x+1) for all real values of ?

Possible Answers:

x^2+3

x+3

x^2+3x

x^2+2x+3

x^2+2x+1

Correct answer:

x^2+2x+3

Explanation:

Whenever there is a function, all you need to do is plug in the value into the function.

f(x)=x^2+2

f(x+1)=(x+1)^2+2

=x^2+x+x+1+2

=x^2+2x+3

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Example Question #151 : Algebraic Functions

If f(x)=-x^2+x , then what is f(x+2) for all real values of ?

Possible Answers:

-x^2+2

x^2+5x+6

-x^2-3x-2

-x^2-4x+4

-x^2-3x+2

Correct answer:

-x^2-3x-2

Explanation:

Whenever there is a function, all you need to do is plug in the value into the function.

f(x)=-x^2+x

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

=-(x^2+2x+2x+4)+x+2

=-x^2-4x-4+x+2

=-x^2-3x-2

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Example Question #1081 : Algebra

If f(x)=3x and g(x)=x^3+1 , what is f(g(3)) ?

Possible Answers:

729

730

Correct answer:

Explanation:

Whenever there is a function, all you need to do is plug in the value into the function. Since this is multi-function, whichever answer we get for the inside function, we plug it into the outer function.

f(x)=3x ; g(x)=x^3+1

f(g(3))=f(3^3+1)=f(28)

f(28)=3(28)=84

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Example Question #1081 : Algebra

If f(x)=x^2-2 and g(x)=x+4 , then what is g(f(x+1)) ?

Possible Answers:

x^2-4x+3

x^2-2x+4

x^2+2x+3

x^2-x-4

x^2-3x-1

Correct answer:

x^2+2x+3

Explanation:

f(x)=x^2-2 and g(x)=x+4

g(f(x+1))=g((x+1)^2-2)=g(x^2+x+x+1-2)=g(x^2+2x-1)

g(x^2+2x-1)=x^2+2x-1+4=x^2+2x+3

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Example Question #1082 : Algebra

If f(x)=3x+2 , then what value of will make f(x)=14 true?

Possible Answers:

Correct answer:

Explanation:

We know f(x)=3x+2 and f(x)=14 . Just set them equal to each other.

3x+2=14 Subtract on both sides.

3x=12 Divide on both sides.

x=4

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Example Question #1082 : Algebra

If f(x)=x^2+17 , then what value of will make f(x)=66 true?

Possible Answers:

$\pm6$

$\pm7$

Correct answer:

$\pm7$

Explanation:

We know f(x)=x^2+17 and f(x)=66 . Just set them equal to each other.

x^2+17=66 Subtract on both sides.

x^2=49 Take square root on both sides and account for also negative answers.

$x=\pm7$

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1074 : Algebra

Example Question #1075 : Algebra

Example Question #1071 : Algebra

Example Question #142 : Algebraic Functions

Example Question #141 : Algebraic Functions

Example Question #151 : Algebraic Functions

Example Question #1081 : Algebra

Example Question #1081 : Algebra

Example Question #1082 : Algebra

Example Question #1082 : Algebra

All SAT Math Resources

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