contestada

What is the inverse of f(x) = (x+6)² for x ≥ -6 where function g is the inverse of function f?
a. g(x) = x+6−−−−√, x≥−6
b. g(x) = x−6−−−−√, x≥6
c. g(x) = x√−6, x≥0
d. g(x) = x√+6, x≥0

Respuesta :

Option C is the correct answer.

Step-by-step explanation:

We have f(x) = (x+6)² for x ≥ -6

That is

             y = (x+6)²

             [tex]x+6=\sqrt{y}\\\\x=\sqrt{y}-6\\\\f^{-1}(x)=\sqrt{x}-6[/tex]

We know that negative of square root value is not defined.

So x should be greater than or equal to zero.

So

             [tex]f^{-1}(x)=\sqrt{x}-6,x\geq 0[/tex]

Option C is the correct answer.