Question

Use algebra to identify the inverse of the function.
F(x)=(x-1)^2-4

Answer 1

`f^(-1)(x)=√(x+4)+1`

Explanation:

`f(x)=(x-1)^2-4\\y=(x-1)^2-4\\`

Swap x and y and solve for y:

`x=(y-1)^2-4\\x+4=(y-1)^2\\√(x+4)=y-1\\√(x+4)+1=y\\f^(-1)(x)=√(x+4)+1`

Hence, the inverse function is
`f^(-1)(x)=√(x+4)+1`