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√+…

Question

asked Nov 4, 2020 136k views

1 Answer

Bmvr · Answer 1 · 2020-11-10T14:45:48+0000

Explanation:

We have f(x) = (x+6)² for x ≥ -6

That is

y = (x+6)²

$x+6=√(y)\\\\x=√(y)-6\\\\f^(-1)(x)=√(x)-6$

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

So x should be greater than or equal to zero.

So

$f^(-1)(x)=√(x)-6,x\geq 0$

Option C is the correct answer.