Question

What is the inverse of f(x)= cube root of x +2.

Answer 1

f(x)=
`\sqrt[3]{x+2}`
to solve for the inverse of a function you do 4 steps:
1. subsitute f(x) with y
2. switch y and x places
3. solve for y
4. subsitute y with f⁻¹(x)

so we have
f(x)=
`\sqrt[3]{x+2}`
subsitute f(x) with y
y=
`\sqrt[3]{x+2}`
switch x and y
x=
`\sqrt[3]{y+2}`
solve for y

x=
`\sqrt[3]{y+2}`
cube both sides

`x^(3)`=y+2
subtract 2 from both sides

`x^(3)-2`=y

subsitute y with f⁻¹(x)
f⁻¹(x)=
`x^(3)-2`



the answer is f⁻¹(x)=
`x^(3)-2`