Question

Composition help

Answer 1

Composition of functions, right?

Answer 2

\[(f0g)(x)\]
\[F(x) =4/(x+1)\]
\[g(x)=4/x\]

Answer 3

yes

Answer 4

Hint: (f o g)(x) = f(g(x))

Answer 5

i got that im lost on what to do after that

Answer 6

i never really liked improper fractions

Answer 7

We don't know if the fraction is proper or improper because we don't know the value of x

Answer 8

But anyway, f(g(x)) means to insert the entire expression for g(x) into the input for f(x)

Answer 9

So you'll end up with:

F(4/x) = 4/((4/x) + 1)

But of course, now you have to simplify that

Answer 10

Good luck simplifying that.

Answer 11

thats want im trying to do, would i multiply the denominator to the other side, and then find x, or would i flip the denominator and multiply it to the top?

Answer 12

Let me show you how to simplify it. We ended up with

\[f\left(\frac{4}{x}\right) = \frac{4}{\frac{4}{x} + 1}\]

So lets concentrate on simplifying the right side.

Answer 13

First to make things a little easier to digest, lets re-write the right side as

\[4 \div \left(\frac{4}{x} + 1\right)\]

Answer 14

Now, remembering PEMDAS, lets simplify whatever is inside the parentheses first. We need to combine 4/x and 1, so re-write 1 = x/x :


\[4 \div \left(\frac{4}{x} + \frac{x}{x}\right)\]

Answer 15

Combining that, we get

\[4 \div \left(\frac{4+x}{x}\right)\]

Now we need to take the reciprocal of the fraction to change the division to a multiplication:

\[4 \dot\ \left(\frac{x}{x+4}\right)\]

Answer 16

Thus we are left with

\[f\left(\frac{4}{x}\right) = \frac{4x}{x+4}\]

Answer 17

thank you