How to inverse this function step by step

f (x) = x-3/5

f (x) = x3-5

Replace f (x)

with y

.

y=x3-5

Interchange the variables.

x=y3-5

Solve for y

.

Since y

is on the right side of the equation, switch the sides so it is on the left side of the equation.

y3-5=x

Add 5

to both sides of the equation.

y3=5+x

Take the cube root of both sides of the equation to eliminate the exponent on the left side.

y=3√5+x

Solve for y

and replace with f-1 (x)

.

Replace the y

with f-1 (x)

to show the final answer.

f-1 (x) = 3√5+x

Set up the composite result function.

f (g (x))

Evaluate f (g (x))

by substituting in the value of g into f

.

(3√5+x) 3-5

Simplify each term.

Remove parentheses around 3√5+x

.

f (3√5+x) = 3√5+x3-5

Rewrite 3√5+x3

as 5+x

.

f (3√5+x) = 5+x-5

Simplify by subtracting numbers.

.

Subtract 5

from 5

.

f (3√5+x) = x+0

Add x

and 0

.

f (3√5+x) = x

Since f (g (x)) = x

, f-1 (x) = 3√5+x is the inverse of f (x) = x3-5

.

f-1 (x) = 3√5+x