The function f is one to one. Find its inverse.

f(x) = 8x^2 - 9, x>=0

inverse is 1/(8x^2-9) then make this true for x>= 0

tell me what you get

To find the inverse of a function, we need to switch the roles of the input and output variables. In other words, we need to solve for x instead of y.

Let's start by replacing f(x) with y:

y = 8x^2 - 9

Next, let's interchange x and y:

x = 8y^2 - 9

Now, let's solve this equation for y. Rearrange the equation to isolate y:

x + 9 = 8y^2

Divide both sides by 8:

(x + 9) / 8 = y^2

Take the square root of both sides (note that we need to consider both the positive and negative square roots):

±√((x + 9) / 8) = y

Therefore, the inverse of the function f(x) = 8x^2 - 9 is:

f^(-1)(x) = ±√((x + 9) / 8)