Question

Which function is the inverse of function g^-1(y)?
g(x)=9x^2–12

Answer 1

The inverse of function g^-1(y) is f(y) = √[(y + 12) / 9].

Explanation:

To find the inverse of function g^-1(y), we start by setting y = g(x):

y = g(x) = 9x^2 - 12

Now we solve for x in terms of y:

y + 12 = 9x^2

x^2 = (y + 12) / 9

x = ±√[(y + 12) / 9]

Since we want to express the inverse function in terms of y, we choose the positive square root:

x = √[(y + 12) / 9]

Finally, we replace x with g^-1(y) to obtain the inverse function:

g^-1(y) = √[(y + 12) / 9]

Therefore, the inverse of function g^-1(y) is f(y) = √[(y + 12) / 9].