algebraic inverses? please??

Question

can you help direct me, please?
show that f(x) and g(x) are inverses of each other.
1) f(x)= 3x+2 ; g(x)=x-2/3. thank you

Answer 1

if they are inverses then f(g(x)= x
so you plug g(x) in for x in the f(x) equation

f(g(x))= 3( x - 2/3) +2
f(g(x)) = 3x -2+2
f(g(x)) = 3x

so i think you typed it in wrong if g(x) = x/3 - 2/3 then they would be inverses.

Answer 2

To prove that

f(x) = 3x + 2
g(x) = (x - 2)/3

are inverses of each other, all you have to do is calculate (fog)(x) or (gof)(x). If you get an answer of x, then they are indeed inverses of each other.

Let's do that.
(fog)(x) = f(g(x))

Now, plug in g(x) in the brackets of the function f.

= f ( (x - 2)/3 )

Now, replace each instance of x in the given function with (x-2)/3.

= 3[(x - 2)/3] + 2

The threes will cancel, since one is the denominator and the other is on the outside of the brackets.

= x - 2 + 2
= x

Therefore, they are inverses of each other.

Answer 3

Here is a hint. Multiplication and division are inverse operations meaning they undo each other.

Answer 4

Inverses:

If:

f(g(x)) = x

and

g(f(x)) = x

then f and g are inverses.