Question

Hello I just need the answer for “What is the inverse for the equation y=x^2+16”

Answer 1

Given:

The given equation is

`y=x^2+16`

Required:

We need to find the inverse for the equation.

Step-by-step explanation:

`\text{ Let y=f\lparen x\rparen and }x=f^(-1)(y)\text{ and substitute }x=f^(-1)(y)\text{ in the given equation.}`
`y=(f^(-1)(y))^2+16`

Substract 16 from both sides of the equation.

`y-16=(f^(-1)(y))^2+16-16`
`y-16=(f^(-1)(y))^2`

Take square root on both sides of the equation.

`\pm√((y-16))=f^(-1)(y)`
`f^(-1)(y)=\pm√((y-16))`

Replace y=x in the equation.

`f^(-1)(x)=\pm√(x-16)`

Final answer:

`f^(-1)(x)=\pm√(x-16)`