Question

What is the inverse of f(x)=(x-5)2 for x≥5 where function g is the inverse of function f?

1) g(x)=x-5----√, x≥5
2) g(x)=x 5----√, x≥-5
3) g(x)=x√-5, x≥0
4) g(x)=x√ 5, x≥0

Answer 1

The inverse function of f(x) = (x - 5)^2 for x ≥ 5 is g(x) = √x + 5, where x ≥ 5.

Step-by-step explanation:

To find the inverse of the function f(x) = (x - 5)^2 for x ≥ 5, we need to switch the roles of x and y and solve for y. Let's start:

1. Replace f(x) with y: y = (x - 5)^2
2. Swap x and y: x = (y - 5)^2
3. Solve for y by taking the square root of both sides: √x = y - 5
4. Add 5 to both sides to isolate y: y = √x + 5

Therefore, the inverse function of f(x) is g(x) = √x + 5, where x ≥ 5.