Question

If f(x) = - x, find f -1(x).f -1(x) = x f -1(x) = -xf -1(x) = √xf -1(x) = 3√x

Answer 1

Given:

`f(x)=-x`

Required:

`We\text{ need to find }f^(-1)(x).`

Step-by-step explanation:

`\text{ Let f\lparen x\rparen=y and }x=f^(-1)(y).`
`Substitute\text{ f\lparen x\rparen=y and }x=f^(-1)(y)\text{ in the equation f\lparen x\rparen=-x.}`
`y=-f^(-1)(y).`

Multiply both sides of the equation by (-1).

`(-1)y=-(-1)f^(-1)(y).`
`-y=f^(-1)(y).`
`f^(-1)(y)=-y`

Replace y=x in the equation.

`f^(-1)(x)=-x`

Final answer:

`f^(-1)(x)=-x`