Find the Inverse:
f(x)=√2x+9
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