Question

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

Answer 1

• g(x) = x² + 20x + 106

Explanation:

Given:

• 
  `f(x) =√(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 =√(g(x)-6)-10`

Solve for g(x):

• 
  `x + 10 = √(g(x)-6)`
• 
  `(x+10)^2=g(x)-6`
• 
  `g(x) = x^2+20x + 100+6`
• 
  `g(x) = x^2+20x + 106`