Answer:
f(x) = 3(x − 9)^2 + 4
To find the inverse of f(x), first we denote: y = 3(x - 9)^2 + 4, we then find a way to express x in term of y.
y = 3(x - 9)^2 + 4
<=> y - 4 = 3(x - 9)^2
<=> (y - 4)/3 = (x - 9)^2
<=> sqrt[(y - 4)/3] = x - 9
<=> x = sqrt[(y - 4)/3] + 9
Denote left side is g(x), and variable y on the right side is x, we have:
g(x) = sqrt[(x - 4)/3] + 9
g(x) is inverse of f(x)
Here, (x - 4)/3 must be not a negative number (because of the definition of square root (sqrt) of a real number)
=> x - 4 >= 0 or x >= 4
=> The restriction domain of g(x), which is the inverse of f(x) is x >= 4
