Question

Find the inverse of the following function.

Answer 1

Answer:

$\Huge \boxed{\mathrm{D}}$

Step-by-step explanation:

$f(x)=8\sqrt{x}$

$\sf Replace \ with \ y.$

$y=8\sqrt{x}$

$\sf Switch \ the \ variables.$

$x= 8\sqrt{y}$

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

$\displaystyle \frac{x}{8} =\sqrt{y}$

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

$\displaystyle (\frac{x}{8} )^2 =y$

$\displaystyle \frac{x^2 }{64} =y$

$\displaystyle f^{-1}(x)=\frac{1}{64} x^2$

Answer 2

Answer:

The inverse is 1/64 x^2 = y   x ≥ 0

Step-by-step 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