Question

Let f(x) = √x-5

Find f^ -1.

Answer 1

`f^(-1)(x)= x^2 + 5 \,,\,\,x\geq 0`

Explanation:

Use the method of swapping x and y and isolating y.

`f(x) = y = √(x-5)\,,\,\,\,x\geq 5,y\geq0\\\\f^(-1):x=√(y-5)\,,\,\,\,y\geq 5, x\geq 0\\x^2 = y-5\\y = x^2 + 5 = f^(-1)(x)\\`

Note that domain/range will be swapped as well.