Question

What is the inverse of f(x) =1/3 x + 2?

Answer 1

Answer:

Step-by-step explanation:

To begin, we will replace f(x) with y, since they mean the same thing, except y does not represent function notation.  We will put it back when we're done.

$y=\frac{1}{3}x+2$

The rules for finding an inverse function algebraically is to switch the x and the y, then solve for the new y.  Our function then becomes, with the variables switched:

$x=\frac{1}{3}y+2$

Begin to isolate the new y by subtracting 2 from both sides:

$x-2=\frac{1}{3}y$

Now multiply both sides by 3:

3(x - 2) = y and

3x - 6 = y

That's the inverse, so now we will put it back into function notation:

$f^{-1}(x)=3x-6$