Question

If g is the inverse of the function f(x) = sqrt(x - 6) - 10 , which of the following is g?

Answer 1

Answer:

• g(x) = x² + 20x + 106

Step-by-step explanation:

Given:

• $f(x) =\sqrt{x-6}-10$

If g(x) is the inverse of f(x), find it.

Swap x with g(x) and f(x) with x:

• $x =\sqrt{g(x)-6}-10$

Solve for g(x):

• $x + 10 = \sqrt{g(x)-6}$
• $(x+10)^2=g(x)-6$
• $g(x) = x^2+20x + 100+6$
• $g(x) = x^2+20x + 106$