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Algebra II : Inverse Functions

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Example Question #41 : Inverse Functions

Determine the inverse of: y=9(6x-2)

Possible Answers:

$y=\frac{1}{54}x+18$

$y=-\frac{1}{54}x+\frac{1}{3}$

$y=\frac{1}{54}x+\frac{1}{3}$

$y=-\frac{1}{54}x+18$

$y=\frac{1}{54}x+3$

Correct answer:

$y=\frac{1}{54}x+\frac{1}{3}$

Explanation:

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

x=9(6y-2)

Distribute the nine through the binomial.

x=9(6y)+9(-2) = 54y-18

x= 54y-18

Add eighteen on both sides.

x+(18)= 54y-18+(18)

x+18=54y

Divide by 54 on both sides.

$\frac{x+18}{54}=\frac{54y}{54}$

The answer is: $y=\frac{1}{54}x+\frac{1}{3}$

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Example Question #42 : Inverse Functions

Determine the inverse of y=2(9-2x) .

Possible Answers:

$y=-\frac{1}{4}x-18$

$y=-\frac{1}{4}x+9$

$y=-\frac{1}{4}x+18$

$y=\frac{1}{4}x+9$

$y=-\frac{1}{4}x+\frac{9}{2}$

Correct answer:

$y=-\frac{1}{4}x+\frac{9}{2}$

Explanation:

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

x=2(9-2y)

Distribute the integer through the binomial.

x=2(9-2y) = 18-4y

x= 18-4y

Add on both sides.

x+(4y)= 18-4y+(4y)

x+4y=18

Subtract on both sides.

4y=-x+18

Divide by four on both sides.

$\frac{4y}{4}=\frac{-x+18}{4}$

Simplify both sides.

The inverse is: $y=-\frac{1}{4}x+\frac{9}{2}$

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Example Question #43 : Inverse Functions

Determine the inverse of: y=-3x-20

Possible Answers:

$y=-\frac{1}{3}x+\frac{20}{3}$

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

$y=\frac{1}{3}x-\frac{20}{3}$

$y=-\frac{1}{3}x-\frac{20}{3}$

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

Correct answer:

$y=-\frac{1}{3}x-\frac{20}{3}$

Explanation:

Interchange the x and y-variable.

x=-3y-20

Add twenty on both sides.

x+20=-3y-20+20

x+20=-3y

Divide both sides by negative three.

$\frac{x+20}{-3}=\frac{-3y}{-3}$

Simplify both sides of the equation.

The answer is: $y=-\frac{1}{3}x-\frac{20}{3}$

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Example Question #44 : Inverse Functions

Determine the inverse of y=-9x-5

Possible Answers:

$y= -\frac{1}{9}x-\frac{5}{9}$

$y= 9x+\frac{5}{9}$

$y= -\frac{1}{9}x+\frac{5}{9}$

$y= -9x+\frac{5}{9}$

$y= -\frac{1}{9}x-\frac{9}{5}$

Correct answer:

$y= -\frac{1}{9}x-\frac{5}{9}$

Explanation:

Interchange the x and y-values.

x=-9y-5

Solve for y. Add five on both sides.

x+(5)=-9y-5+(5)

The equation becomes: x+5 =-9y

Divide by negative nine on both sides.

$\frac{x+5}{-9} =\frac{-9y}{-9}$

The answer is: $y= -\frac{1}{9}x-\frac{5}{9}$

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Example Question #45 : Inverse Functions

Determine the inverse: y=3(x-10)

Possible Answers:

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

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

$y=\frac{1}{3}x+30$

$y=-\frac{1}{3}x+30$

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

Correct answer:

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

Explanation:

Interchange both the x and y- variables.

x=3(y-10)

Solve for y. Distribute the three through both terms of the binomial.

x=3y-30

Add 30 on both sides.

x+30=3y-30+30

x+30=3y

Divide by three on both sides.

$\frac{x+30}{3}=\frac{3y}{3}$

Simplify both sides.

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

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Example Question #46 : Inverse Functions

Determine the inverse function: y=9x+26

Possible Answers:

$y=-9x-\frac{26}{9}$

$y=\frac{1}{9}x-\frac{26}{9}$

$y=-\frac{1}{9}x+\frac{26}{9}$

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

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

Correct answer:

$y=\frac{1}{9}x-\frac{26}{9}$

Explanation:

Interchange the x and y-variables.

x=9y+26

Solve for y. Subtract 26 from both sides.

x-26=9y+26-26

The equation becomes:

x-26=9y

Divide by nine on both sides.

$\frac{x-26}{9}=\frac{9y}{9}$

Simplify both fractions.

The answer is: $y=\frac{1}{9}x-\frac{26}{9}$

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Example Question #241 : Introduction To Functions

Determine the inverse of: y= 7x-4

Possible Answers:

$y=-7x+\frac{4}{7}$

$y=\frac{1}{7}x+\frac{4}{7}$

y=-7x+4

$y=\frac{1}{7}x-\frac{4}{7}$

$y=\frac{4}{7}x-\frac{4}{7}$

Correct answer:

$y=\frac{1}{7}x+\frac{4}{7}$

Explanation:

Interchange the x and y variables and solve for y.

x= 7y-4

Add four on both sides.

x+4= 7y-4+4

Simplify both sides.

x+4= 7y

Divide by seven on both sides.

$\frac{x+4}{7}= \frac{7y}{7}$

The answer is: $y=\frac{1}{7}x+\frac{4}{7}$

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Example Question #48 : Inverse Functions

Determine the inverse of: y=-(x+6)

Possible Answers:

y=-6x

y=x-6

y=-x+6

y=-x-6

y=x+6

Correct answer:

y=-x-6

Explanation:

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

x=-(y+6)

Divide by negative one on both sides.

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

Simplify both sides.

-x = y+6

Subtract six from both sides.

-x-6 = y+6-6

The answer is: y=-x-6

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Example Question #49 : Inverse Functions

Determine the inverse of: y= 2x-50

Possible Answers:

$y=-\frac{1}{2}x-25$

$y=\frac{1}{2}x-25$

$y=-\frac{1}{2}x-50$

$y=\frac{1}{2}x+25$

y=-2x-50

Correct answer:

$y=\frac{1}{2}x+25$

Explanation:

Interchange the x and y-variables.

x= 2y-50

Add 50 on both sides.

x+50= 2y-50+50

The equation becomes:

x+50= 2y

Divide both sides by two and split the fraction.

$\frac{x+50}{2}=\frac{ 2y}{2}$

The answer is: $y=\frac{1}{2}x+25$

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Example Question #50 : Inverse Functions

Determine the inverse: y=-4x-19

Possible Answers:

$4x-\frac{19}{4}$

$-\frac{1}{4}x+\frac{19}{4}$

$-\frac{1}{4}x-\frac{19}{4}$

$-\frac{1}{4}x-19$

$\frac{1}{4}x-\frac{4}{19}$

Correct answer:

$-\frac{1}{4}x-\frac{19}{4}$

Explanation:

Interchange the x and y-variables.

x=-4y-19

Add 19 on both sides.

x+19=-4y-19+19

x+19=-4y

Divide by negative four on both sides.

$\frac{x+19}{-4}=\frac{-4y}{-4}$

Simplify both sides.

The answer is: $-\frac{1}{4}x-\frac{19}{4}$

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Algebra II : Inverse Functions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #41 : Inverse Functions

Example Question #42 : Inverse Functions

Example Question #43 : Inverse Functions

Example Question #44 : Inverse Functions

Example Question #45 : Inverse Functions

Example Question #46 : Inverse Functions

Example Question #241 : Introduction To Functions

Example Question #48 : Inverse Functions

Example Question #49 : Inverse Functions

Example Question #50 : Inverse Functions

All Algebra II Resources

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