The function f is one to one. Find its inverse.
f(x) = 8x^2 - 9, x>=0
To find the inverse of a function, we need to switch the roles of x and y and solve for y.
Step 1: Replace f(x) with y.
y = 8x^2 - 9
Step 2: Swap the x and y variables.
x = 8y^2 - 9
Step 3: Solve this equation for y.
x + 9 = 8y^2
Step 4: Divide both sides of the equation by 8.
(x + 9) / 8 = y^2
Step 5: Take the square root of both sides.
√((x + 9) / 8) = y
Step 6: Simplify the expression.
y = ± √((x + 9) / 8)
Therefore, the inverse of the given function f(x) = 8x^2 - 9 is f^(-1)(x) = ± √((x + 9) / 8).