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Algebra II : Inverse Functions

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Example Question #51 : Inverse Functions

Determine $f^{-1}(x)$ if f(x)= 4x-80 .

Possible Answers:

$\frac{1}{4}x+20$

$\frac{1}{20}x-\frac{1}{20}$

$\frac{1}{4}x-20$

$-\frac{1}{4}x-20$

$\frac{1}{20}x-20$

Correct answer:

$\frac{1}{4}x+20$

Explanation:

Replace the f(x) term with the y-variable.

y= 4x-80

Interchange the x and y-variables.

x= 4y-80

Add 80 on both sides.

x+80= 4y-80+80

x+80= 4y

Divide by four on both sides.

$\frac{x+80}{4}= \frac{4y}{4}$

Simplify both sides.

$f^{-1}(x)=y=\frac{1}{4}x+\frac{80}{4}$

The answer is: $\frac{1}{4}x+20$

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Example Question #52 : Inverse Functions

Determine the inverse function of y=-3x+24

Possible Answers:

$y=-\frac{1}{3}x +8$

y=-3x -8

$y=-\frac{1}{3}x +\frac{8}{3}$

$y=-3x -\frac{8}{3}$

$y=-\frac{1}{3}x -8$

Correct answer:

$y=-\frac{1}{3}x +8$

Explanation:

Interchange the x and y-variables.

x=-3y+24

Subtract 24 from both sides.

x-24=-3y+24-24

The equation becomes:

x-24=-3y

Divide by negative three on both sides.

$\frac{x-24}{-3}=\frac{-3y}{-3}$

Simplify both sides of the equation.

The answer is: $y=-\frac{1}{3}x +8$

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Example Question #251 : Functions And Graphs

Find the inverse of: -3x+9y =4

Possible Answers:

$y=-3x-\frac{4}{3}$

$y=\frac{3}{4}x-\frac{3}{4}$

$y=3x-\frac{4}{3}$

$y=\frac{3}{2}x-\frac{3}{2}$

$y=3x-\frac{2}{3}$

Correct answer:

$y=3x-\frac{4}{3}$

Explanation:

Interchange the x and y-variables.

-3y+9x =4

Solve for . Subtract on both sides.

-3y+9x-9x =4-9x

-3y = -9x+4

Divide by negative three on both sides.

$\frac{-3y}{-3} = \frac{-9x+4}{-3}$

Simplify both sides.

The answer is: $y=3x-\frac{4}{3}$

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Example Question #252 : Functions And Graphs

Find the inverse of f(x)= -3x+4

Possible Answers:

$y(x)=\frac{3+x}{4}$

None of these.

$y(x)=\frac{3-x}{4}$

$y(x)=\frac{4+x}{3}$

$y(x)=\frac{4-x}{3}$

Correct answer:

$y(x)=\frac{4-x}{3}$

Explanation:

y= -3x+4

Switch the variables and solve for Y again:

x= -3y+4

Subtract 4 from both sides:

x-4= -3y

Divide both sides by -3:

$y=-\frac{(x-4)}{3}$

$\boldsymbol{y=\frac{4-x}{3}}$

*Note the negative sign was distributed in the last step.

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Example Question #253 : Functions And Graphs

Determine the inverse of the following function: $y=\frac{1}{8}x-2$

Possible Answers:

y= -8x-16

y= 8x+2

y= -8x-12

y= 8x+16

y= 8x-8

Correct answer:

y= 8x+16

Explanation:

Interchange the x and y-variables.

$x=\frac{1}{8}y-2$

Add two on both sides.

$x+2=\frac{1}{8}y-2+2$

$x+2=\frac{1}{8}y$

Multiply both sides by eight to isolate the y-variable.

$8(x+2)=\frac{1}{8}y \cdot 8$

The equation becomes:

y=8(x+2) = 8x+16

The answer is: y= 8x+16

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Example Question #254 : Functions And Graphs

Determine the inverse of: y=-2(4-x)

Possible Answers:

$y=\frac{1}{2}x+2$

y=2x+2

$y=\frac{1}{2}x+8$

$y=\frac{1}{2}x+4$

y=4x+2

Correct answer:

$y=\frac{1}{2}x+4$

Explanation:

Interchange the x and y-variables.

x=-2(4-y)

Solve for y. Divide by negative two on both sides.

$\frac{x}{-2}=\frac{-2(4-y)}{-2}$

Simplify the right side.

$-\frac{1}{2}x =4-y$

Add y on both sides.

$-\frac{1}{2}x +y=4-y+y$

$-\frac{1}{2}x +y=4$

Add $\frac{1}{2}x$ on both sides.

$-\frac{1}{2}x +y+\frac{1}{2}x=4+\frac{1}{2}x$

The answer is: $y=\frac{1}{2}x+4$

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Example Question #255 : Functions And Graphs

Determine the inverse of: y=3(x-4)

Possible Answers:

$y=\frac{1}{3}x+\frac{1}{12}$

$y=\frac{1}{3}x+\frac{1}{3}$

$y=\frac{1}{3}x+6$

$y=\frac{1}{3}x+\frac{4}{3}$

$y=\frac{1}{3}x+4$

Correct answer:

$y=\frac{1}{3}x+4$

Explanation:

Interchange the x and y variables.

x=3(y-4)

Solve for y.

x=3y-12

Add 12 on both sides of the equation.

x+12=3y-12+12

x+12=3y

Divide both sides by three.

$\frac{x+12}{3}=\frac{3y}{3}$

The answer is: $y=\frac{1}{3}x+4$

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Example Question #256 : Functions And Graphs

Determine the inverse function: y=9-2x

Possible Answers:

$y=-\frac{1}{2}x+18$

$y=-\frac{1}{2}x+\frac{9}{2}$

$y=-\frac{1}{2}x+\frac{2}{9}$

$y=-\frac{1}{2}x+9$

$y=-\frac{1}{2}x-18$

Correct answer:

$y=-\frac{1}{2}x+\frac{9}{2}$

Explanation:

Interchange the x and y variables.

x=9-2y

Solve for y. Subtract nine on both sides.

x-9=9-2y-9

x-9=-2y

Divide by negative two on both sides.

$\frac{x-9}{-2}=\frac{-2y}{-2}$

Simplify both sides.

The answer is: $y=-\frac{1}{2}x+\frac{9}{2}$

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Example Question #51 : Inverse Functions

What is $f^{-1}(5)$ if x-f(x)=5 ?

Possible Answers:

$\frac{1}{5}$

Correct answer:

Explanation:

The notation $f^{-1}(5)$ designates the inverse function at x=5 .

Replace the f(x) term with .

x-y=5

Interchange the and values.

y-x=5

Solve for . Add on both sides.

y-x+x=5+x

The inverse function is: y=x+5

Substitute x=5 into the inverse function.

y=x+5 = 5+5 =10

The answer is:

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Example Question #258 : Functions And Graphs

Find the inverse of: y=-6x+7

Possible Answers:

$y=-\frac{1}{6}x-\frac{7}{6}$

$y=-\frac{1}{6}x+7$

$y=-\frac{1}{6}x+\frac{7}{6}$

$y=-\frac{1}{6}x-7$

$y=-\frac{7}{6}x+\frac{1}{6}$

Correct answer:

$y=-\frac{1}{6}x+\frac{7}{6}$

Explanation:

Interchange the x and y variables.

x=-6y+7

Solve for y. Subtract seven on both sides.

x-7=-6y+7-7

x-7=-6y

Divide by negative six on both sides.

$\frac{x-7}{-6}=\frac{-6y}{-6}$

The answer is: $y=-\frac{1}{6}x+\frac{7}{6}$

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Algebra II : Inverse Functions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #51 : Inverse Functions

Example Question #52 : Inverse Functions

Example Question #251 : Functions And Graphs

Example Question #252 : Functions And Graphs

Example Question #253 : Functions And Graphs

Example Question #254 : Functions And Graphs

Example Question #255 : Functions And Graphs

Example Question #256 : Functions And Graphs

Example Question #51 : Inverse Functions

Example Question #258 : Functions And Graphs

All Algebra II Resources

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