Question

What is the inverse of f(x)=(xˆ’5)2 for x¥5 where function g is the inverse of function f?

Answer 1

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

Step-by-step explanation:

To find the inverse of the function f(x) = (x - 5)2, we need to interchange the roles of x and y and solve for y. Let's call the inverse function g(x) instead of g. So, we have y = (x - 5)2. Interchanging x and y, we get x = (y - 5)2. Now, solve this equation for y to find g(x).

1. Take the square root of both sides of the equation: √x = y - 5.
2. Add 5 to both sides of the equation: √x + 5 = y.

Therefore, the inverse function g(x) of f(x) = (x - 5)2 is g(x) = √x + 5.

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