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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #29 : Inverse Functions

Find $f^{-1}(x)$ if f(x)= 9x-3 .

Possible Answers:

$y= \frac{1}{9x-3}$

$y=\frac{1}{9}x+\frac{1}{3}$

$y=\frac{1}{9}x-\frac{1}{3}$

$y=-\frac{1}{9}x-\frac{1}{3}$

$y=\sqrt{9x-3}$

Correct answer:

$y=\frac{1}{9}x+\frac{1}{3}$

Explanation:

To solve for the inverse function, first replace f(x) with .

The equation becomes: y= 9x-3

Interchange the variables.

x=9y-3

Add three on both sides.

x+3=9y

Divide by nine on both sides.

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

Simplify both sides of the equation.

The answer is: $y=\frac{1}{9}x+\frac{1}{3}$

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Example Question #22 : Inverse Functions

Find the inverse of the function: $y=-\frac{1}{4}x-6$

Possible Answers:

$y=-4x-\frac{2}{3}$

y=-4x-24

y=-4x+24

$y=-4x-\frac{3}{2}$

$\textup{The inverse is not given.}$

Correct answer:

y=-4x-24

Explanation:

In order to find the inverse, interchange the x and y-variables.

$x=-\frac{1}{4}y-6$

Solve for y. Add 6 on both sides of the equation.

$x+6=-\frac{1}{4}y-6+6$

The equation becomes:

$x+6=-\frac{1}{4}y$

Multiply by negative four on both sides to isolate the y-variable.

$-4(x+6)=-4(-\frac{1}{4}y)$

Simplify both sides of the equation.

The answer is: y=-4x-24

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Example Question #31 : Inverse Functions

Find the inverse of the equation: y=6x-14

Possible Answers:

y=-6x-14

$y=\frac{1}{6}x -\frac{7}{3}$

$y=\frac{1}{6}x +\frac{7}{3}$

$y=-\frac{1}{6}x -\frac{7}{3}$

y=6x-14

Correct answer:

$y=\frac{1}{6}x +\frac{7}{3}$

Explanation:

To solve for the inverse, first interchange the x and y-variables.

x=6y-14

Solve for y. Add 14 on both sides.

x+14=6y-14+14

Simplify the right side.

x+14=6y

Divide by six on both sides.

$\frac{x+14}{6}=\frac{6y}{6}$

Simplify both sides of the equation.

The answer is: $y=\frac{1}{6}x +\frac{7}{3}$

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Example Question #32 : Inverse Functions

Find the inverse of the following function: $y=-\frac{2}{3}x+2$

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Interchange the x and y-variables.

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

Solve for y. Subtract two from both sides.

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

Simplify the right side.

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

Multiply both sides by the reciprocal of the coefficient in front of the y-variable.

$-\frac{3}{2}(x-2)=-\frac{2}{3}y\cdot -\frac{3}{2}$

Simplify both sides. Distribute the fraction on the left side.

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

The answer is: $y=-\frac{3}{2}x+3$

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Example Question #33 : Inverse Functions

Solve for the inverse: $y=\frac{1}{6}x+6$

Possible Answers:

y=6x-36

y=-6x-6

y=6x+36

y=-6x-36

y=-6x+6

Correct answer:

y=6x-36

Explanation:

Interchange the x and y-variables, and solve for y.

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

Subtract six from both sides.

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

Simplify the right side.

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

In order to isolate the y-variable, we will need to multiply six on both sides.

$6(x-6)=\frac{1}{6}y\cdot 6$

Simplify both sides. Distribute the integer through the binomial on the left.

6x-36=y

The answer is: y=6x-36

Report an Error

Example Question #231 : Functions And Graphs

Find the inverse of the function: y=4x+3

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Interchange the x and y-variables.

x=4y+3

Solve for y. Subtract three from both sides.

x-3=4y+3-3

Simplify the right side.

x-3=4y

Divide by four on both sides.

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

Simplify both sides.

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

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Example Question #35 : Inverse Functions

Find the inverse of: y=x^3+5

Possible Answers:

$y=\sqrt[3]{x}-5$

$y=-\sqrt[3]{x-5}$

$y=\sqrt[3]{3x}-5$

$y=\frac{\sqrt[3]{5}}{5}x+\frac{3}{5}$

$y=\sqrt[3]{x-5}$

Correct answer:

$y=\sqrt[3]{x-5}$

Explanation:

Interchange the x and y-variables. The equation becomes:

x=y^3+5

Subtract five from both sides.

x-5=y^3+5-5

x-5=y^3

Take the cubed root on both sides. This will eliminate the cubed exponent.

$\sqrt[3]{x-5}=\sqrt[3]{y^3}$

The answer is: $y=\sqrt[3]{x-5}$

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Example Question #36 : Inverse Functions

Determine the inverse of: $y=\frac{2}{5}x-\frac{1}{2}$

Possible Answers:

$y=\frac{5}{2}x+\frac{5}{4}$

$y=-\frac{5}{2}x-\frac{1}{2}$

$y=\frac{5}{2}x+\frac{1}{2}$

$y=\frac{5}{2}x-\frac{5}{4}$

$y=-\frac{5}{2}x+\frac{1}{2}$

Correct answer:

$y=\frac{5}{2}x+\frac{5}{4}$

Explanation:

Interchange the x and y-variables.

$x=\frac{2}{5}y-\frac{1}{2}$

Solve for y. Add one-half on both sides.

$x+\frac{1}{2}=\frac{2}{5}y-\frac{1}{2}+\frac{1}{2}$

Simplify both sides.

$x+\frac{1}{2}=\frac{2}{5}y$

Multiply five over two on both sides in order to isolate the y-variable.

$\frac{5}{2}(x+\frac{1}{2})=\frac{2}{5}y\cdot \frac{5}{2}$

Apply the distributive property on the left side. The right side will reduce to just a lone y-variable.

The answer is: $y=\frac{5}{2}x+\frac{5}{4}$

Report an Error

Example Question #37 : Inverse Functions

Determine the inverse of: y=-2x-1

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Interchange the x and y-variables and solve for y.

x=-2y-1

Add one on both sides.

x+1=-2y-1+1

x+1=-2y

Divide by negative two on both sides.

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

Simplify the fractions.

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

Report an Error

Example Question #36 : Inverse Functions

Determine the inverse: y= 10x+3

Possible Answers:

$y=\frac{3}{10}x-3$

$y=\frac{1}{10}x-\frac{3}{10}$

$y=\frac{1}{10}x+\frac{3}{10}$

$y=\frac{1}{10}x-3$

$y=-\frac{1}{10}x-\frac{3}{10}$

Correct answer:

$y=\frac{1}{10}x-\frac{3}{10}$

Explanation:

In order to find the inverse of this function, interchange the x and y-variables.

x= 10y+3

Subtract three from both sides.

x-3= 10y+3-3

Simplify the equation.

x-3= 10y

Divide by ten on both sides.

$\frac{x-3}{10}= \frac{10y}{10}$

Simplify both sides.

The answer is: $y=\frac{1}{10}x-\frac{3}{10}$

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #29 : Inverse Functions

Example Question #22 : Inverse Functions

Example Question #31 : Inverse Functions

Example Question #32 : Inverse Functions

Example Question #33 : Inverse Functions

Example Question #231 : Functions And Graphs

Example Question #35 : Inverse Functions

Example Question #36 : Inverse Functions

Example Question #37 : Inverse Functions

Example Question #36 : Inverse Functions

All Algebra II Resources

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