Question

Find an equation for the inverse of the function.

f(x)=2-3x/4

Answer 1

find value of x

Answer 2

move everything on left side excpt x

Answer 3

f(x)-2=-3x/4
(f(x)-2)*(-4)/3=x
now replace x by f^-1(x)
and f(x) by x

Answer 4

1st step - write in terms of y

y=2-3x/4

2nd step (interchange x and y):

x=2-3y/4

3rd stop - solve for y

x -2=-3y/4
-3y/4 = x - 2
-3y = 4(x-2)
y=-4(x-2)/3

This is your inverse.

Check you work by plugging in for x your original equation, f(x), you should get x back as result. That is what inverse means, you give it f(x) and you get x back. You give it a x and you get f(x) back:

$$
y=-4(2-\cfrac{3x}{4}-2)/3\\
=\cfrac{3x}{3}=x
$$

You can also plug in for x the inverse we just derived into your original equation and you will get back f(x). I'll let you check that one.