if f(x) = -3x + 3 find f-1(x)

Question

the f in the second place should be written like this

f^-1(x)

Answer 1

f^-1(x) means the "inverse" of f. Inverse can have many meanings depending on context in math, but here it means the inverse function. If you are confused about the concept of an inverse function, I would recorded checking your textbook or googling. It's more then I can explain here. But in short, to find an inverse function, you swap all "x" and "y" variables in the equation. Remember that y = f(x), that is y and f(x) are interchangeable.

So in this case we have the equation (or function):

y = -3x + 3

If we swap all the "x" variables with "y" variables, we get:

x = -3y + 3

This is technically the answer; however, it's not in the right form. The right form is for "y" to be isolated. So let's do some algebra:

x = -3y + 3

x - 3 = -3y

(x - 3) / -3 = y

(3 - x) / 3 = y

y = (3 - x) / 3

And that is your inverse function:

f^-1(x) = (3 - x) / 3

Again, I would recommend looking up the concept of an "inverse function" (as well as "function composition") to better understand why this works.