Question

Find the inverse of the following function. f(x)=8 sqaure root x, for x greater than or equal to 0

Answer 1

Answer:

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

Step-by-step explanation:

f(x) = 8√x    for  x≥0

y = 8√x

To find the inverse you have to replace every x with a y and replace every y with an x .

x = 8√y

$\frac{x}{8} = \sqrt{y} \\\\(\frac{x}{8} )^{2} = (\sqrt{y} )^{2} \\\\\frac{x^2}{8^2} = y\\\\y=\frac{x^2}{64} \\\\f^{-1}(x)=\frac{x^2}{64}$