The inverse of the function f(x)=(x+6)² for x≥–6 will be g(x) = √(x) - 6 , x ≥ 0 so option (A) must be correct.
What is an inverse function?
In relation to the original function f, the inverse function is denoted by the symbol [tex]f^{-1}[/tex], and both the original function's domain and its range are transformed into the inverse function's domain and range, respectively.
In other meaning, if you solve a function for x instant of y then that function will be the inverse function.
For example y = f(x) then x = f(y) will be inverse.
Given function is f(x)=(x+6)²
Let f(x) = y ⇒ y = (x+6)²
Interchange x and y in function
x = ( y + 6 )²
√x = y + 6
y = √x - 6
g(x) = √x - 6 so it will be the inverse of the function f(x)=(x+6)².
For more about the inverse function,
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