SOLUTION: can you tell me i have been trying to get the answer and I just can't get it . This two function with the works given f(x)= 1/x-2 G(x)=4/x. Find (fog)(x) and using the same funct

Question 293389: can you tell me i have been trying to get the answer and I just can't get it . This two function with the works given f(x)= 1/x-2 G(x)=4/x. Find (fog)(x) and using the same function find (gof)(x). thank you in advance
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
f(x) =

g(x) =

Find (fog)(x)

Find (gof)(x)

First we'll do (fog)(x):

(fog)(x) = f(g(x))

g(x) =

f(x) =

f(g(x)) becomes f()

You are replacing x with g(x) in f(x) which means you are replacing x with in f(x).

Your equation f(x) becomes f()

Since f(x) = and you are replacing x with (4/x), then your equation becomes:

f() =

If you multiply numerator and denominator of this expression by x, then you get:

f() = which becomes:

f() =

To test this out, pick a number for x.

Let x = 5.

f(g()) = = = = -1

Solve separately to confirm the answer is good.

Solve for g(x) = to get g(4) = = 1

You now have g(x) = 1

Solve for f(g(x)) = f(1) = = = = -1

We get a match again, so the function f(g(x)) was translated correctly.

Next we'll do (gof)(x).

That's equivalent to g(f(x)).

f(x) =

g(x)=

g(f(x)) is therefore equal to

Multiply numerator and denominator of this equation by (x-2) to get:

g(f(x)) = = 4x-8

To confirm we'll do g(x) separately, and then do f(g(x)) from the answer, and we'll do f(g(x)) using the combined formula to see if they match.

We'll choose x = 5 again.

g(f(x)) = 4x-8 = 4*5 - 8 = 20 - 8 = 12

Solve for f(x) separately to get f(x) = = =

solve for g(f(x)) = g() to get g() = = = 12.

The answers match.

Those should be your answers:

f(g(x)) =

g(f(x)) = 4x-8

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