What is the domain restriction that will allow you to find an inverse of the function f(x) = 3(x − 9)2 + 4?

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

the expression (1.26)2t reveals the approximate rate of increases in the number of plants semiannually.

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