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)