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SAT Math : How to find f(x)

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Example Questions

Example Question #111 : How To Find F(X)

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

Possible Answers:

730

729

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 #112 : How To Find F(X)

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

Possible Answers:

x^2+2x+3

x^2-3x-1

x^2-x-4

x^2-4x+3

x^2-2x+4

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 #113 : How To Find F(X)

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 #114 : How To Find F(X)

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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Example Question #111 : How To Find F(X)

If $f(x)=\left | x+1\right |$ then what value of will make f(x)=12 true?

Possible Answers:

$\pm13$

11, -13

$\pm11$

Correct answer:

11, -13

Explanation:

We know that $f(x)=\left | x+1\right |$ and f(x)=12 . Just set them equal to each other.

$\left | x+1\right |=12$ Remember to account for negative values.

x+1=12 Subtract on both sides.

x=11

x+1=-12 Subtract on both sides.

x=-13

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Example Question #2862 : Sat Mathematics

If f(x)=x+5 and g(x)=x^2 then what value of will make f(g(x))=30 true?

Possible Answers:

$\pm5$

Correct answer:

$\pm5$

Explanation:

We know f(g(x))=30 so we need to apply substitutions to solve for .

f(g(x))=f(x^2)=x^2+5=30 Subtract on both sides.

x^2=25 Take square root on both sides and account for negative values.

$x=\pm5$

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Example Question #2863 : Sat Mathematics

If f(x)=x-1, g(x)=x^2+x , then what value of will make f(g(x))=5

Possible Answers:

2,-3

$\pm2, \pm3$

-3, 2

$\pm3$

$\pm2$

Correct answer:

-3, 2

Explanation:

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

We know f(g(x))=5 so let's make the substitution.

f(g(x))=f(x^2+x)=x^2+x-1=5 This is a quadratic so subtract on both sides.

x^2+x-6=0 Factor.

(x+3)(x-2)=0 Solve individually.

x=-3, 2

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Example Question #2864 : Sat Mathematics

Define f(x) = 7x - 15 .

How can g(x) be defined so that $(f \circ g) (x) = 14x + 4$ ?

Possible Answers:

$g(x) = \frac{14x+ 4}{7x-15}$

$g(x) = 2x + \frac{ 19}{7}$

$g(x) = \frac{7x-15}{14x+ 4}$

$g(x) = \frac{1}{2}x - \frac{ 11}{14}$

g(x)= -7x - 19

Correct answer:

$g(x) = 2x + \frac{ 19}{7}$

Explanation:

By definition,

$(f \circ g) (x) = f [g(x)]$ ,

f [g(x)] = 14x + 4

f(x) = 7x - 15 ,

it follows that

f [g(x)] =7g(x) - 15 ,

and, substituting,

7g(x) - 15 = 14x + 4

Solving for g(x) by isolating this expression:

7g(x) - 15 + 15 = 14x + 4 + 15

7g(x) = 14x + 19

$7g(x) \div 7 = (14x + 19) \div 7$

$g(x) = \frac{14x + 19}{7}$

$g(x) = 2x + \frac{ 19}{7}$ .

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Example Question #2865 : Sat Mathematics

Define $f(x) = x^{2} + 4$ .

How can g(x) be defined so that $(f \circ g) (x) = 6x$ ?

Possible Answers:

$g(x) = \sqrt{ 6x - 4}$

$g(x) = -4 + \sqrt{ 6x }$

$g(x) = \frac{1}{6} \sqrt{ x - 4}$

$g(x) = \sqrt{ \frac{x - 4}{6}}$

$g(x) = 6 \sqrt{ x - 4}$

Correct answer:

$g(x) = \sqrt{ 6x - 4}$

Explanation:

By definition,

$(f \circ g) (x) = f [g(x)]$ ,

f [g(x)] = 6x

$f(x) = x^{2} + 4$ ,

it follows that

$f [g(x)] = [g(x)]^{2} + 4$ ,

and, substituting,

$[g(x)]^{2} + 4 = 6x$

Solving for g(x) by isolating this expression:

$[g(x)]^{2} + 4 = 6x$

$[g(x)]^{2} = 6x - 4$

Taking the square root of both sides:

$g(x) = \pm \sqrt{ 6x - 4}$

Either $g(x) =- \sqrt{ 6x - 4}$ , which is not among the given choices, or $g(x) = \sqrt{ 6x - 4}$ , which is.

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Example Question #2866 : Sat Mathematics

Define $f(x) = \sqrt{3x+ 21 }$ .

How can g(x) be defined so that $(f \circ g) (x) = 9x$ ?

Possible Answers:

$g(x) = 9 x^{2} -49$

$g(x) = 27 x^{2} - 21$

$g(x) = 9 x^{2} + 42x +49$

$g(x) = 9 x^{2} -42x +49$

$g(x) = 27 x^{2} - 7$

Correct answer:

$g(x) = 27 x^{2} - 7$

Explanation:

By definition,

$(f \circ g) (x) = f [g(x)]$ ,

f [g(x)] = 9x

$f(x) = \sqrt{3x+ 21}$ ,

it follows that

$f [g(x)] = \sqrt{3 [g(x)]+ 21}$ ,

and, substituting,

$\sqrt{3 [g(x)]+ 21 } = 9x$

Solving for g(x) by isolating this expression:

$\left (\sqrt{3 [g(x)]+ 21} \right ) ^{2}=\left ( 9x \right )^{2}$

Applying the Power of a Product Rule:

$3 [g(x)]+ 21= 9^{2} \cdot x^{2}$

$3 [g(x)]+ 21= 81 x^{2}$

$3 [g(x)]+ 21- 21 = 81 x^{2} - 21$

$3 [g(x)] = 81 x^{2} - 21$

$\frac{3 [g(x)] }{3} = \frac{ 81 x^{2} - 21 }{3}$

$g(x) = 27 x^{2} - 7$

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SAT Math : How to find f(x)

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #111 : How To Find F(X)

Example Question #112 : How To Find F(X)

Example Question #113 : How To Find F(X)

Example Question #114 : How To Find F(X)

Example Question #111 : How To Find F(X)

Example Question #2862 : Sat Mathematics

Example Question #2863 : Sat Mathematics

Example Question #2864 : Sat Mathematics

Example Question #2865 : Sat Mathematics

Example Question #2866 : Sat Mathematics

All SAT Math Resources

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