Question

Find the inverse of each function:

g(x)=
`(-5x+5)/(2)`
A. g^{-1}[/tex](x)=
`(5-2x)/(5)`
B. g^{-1}[/tex](x)=
`4+(4)/(3)x`
C. g^{-1}[/tex](x)=
`(10-x)/(2)`
D. g^{-1}[/tex](x)=
`-4+(1)/(3)x`

Answer 1

Explanation:

Replace g(x) with y, then switch the x and y variables:

`x=(-5y+5)/(2)`

Solve for the new y value, multiply by 2:

`2x=-5y+5`

Subtract 5 on both sides:

`2x-5=-5y`

Divide by -5 on both sides:

`-(2x-5)/(5) =y`

Distribute the negative sign and rearrange:

`(-2x+5)/(5) =(5-2x)/(5) =g^-^1(x)`

Answer 2

• A. g⁻¹(x) = (5 - 2x)/5

Explanation:

Given function

• g(x) = (-5x + 5)/2

Find

• the inverse of g(x)

Solution

Substitute x with y and g(x) with x and then solve for y:

• x = (-5y + 5) /2
• 2x = -5y + 5
• 5y = -2x + 5
• y = (-2x + 5)/5
• y = (5 - 2x)/5

Replace y with g⁻¹(x)

• g⁻¹(x) = (5 - 2x)/5

Correct choice is A