Question

How to inverse this function step by step f(x)=x-3/5

Answer 1

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