Question

Find the inverse of the following function.

Answer 1

`\Huge \boxed{\mathrm{D}}`

Explanation:

`f(x)=8√(x)`

`\sf Replace \ with \ y.`

`y=8√(x)`

`\sf Switch \ the \ variables.`

`x= 8√(y)`

`\sf Divide \ both \ sides \ of \ the \ equation \ by \ 8.`

`\displaystyle (x)/(8) =√(y)`

`\sf Square \ both \ sides \ of \ the \ equation.`

`\displaystyle ((x)/(8) )^2 =y`

`\displaystyle (x^2 )/(64) =y`

`\displaystyle f^(-1)(x)=(1)/(64) x^2`

Answer 2

The inverse is 1/64 x^2 = y x ≥ 0

Explanation:

f(x) = 8 sqrt(x)

y = 8 sqrt(x)

Exchange x and y

x = 8 sqrt (y)

Solve for y

Divide each side by 8

1/8 x = sqrt(y)

Square each side

(1/8 x)^2 = (sqrt(y))^2

1/64 x^2 = y

The inverse is 1/64 x^2 = y x ≥ 0

since x ≥0 in the original function