Find the Inverse:


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

Let's begin by replacing f(x) with y in the original equation:

y = √(2x + 9)

Next, swap x and y:

x = √(2y + 9)

Now, isolate y by squaring both sides:

x² = 2y + 9

Rearrange the equation to solve for y:

2y = x² - 9

Divide both sides by 2:

y = (x² - 9)/2

Therefore, the inverse function of f(x) = √(2x + 9) is:

f^(-1)(x) = (x² - 9)/2