Question

Find the inverse of the function. Is the inverse a function?
f(x)=2x-9

Answer 1

To find the inverse of a function, we need to switch the roles of x and y and solve for y.

Let's start by switching the roles of x and y.
x = 2y - 9

Now, let's solve for y:
x + 9 = 2y
2y = x + 9
y = (x + 9)/2

So, the inverse of f(x) = 2x - 9 is f^(-1)(x) = (x + 9)/2.

The inverse is a function since for each value of x in the domain of f(x), there is a unique value of y in the range of f(x), and vice versa.