Question

let f(x)=x^2+7 and g(x)=x+3/x. Find (g*f)(-5)

Answer 1

1027/32

Answer 2

Oh, I'm sorry. That's not on my list. I can post the selections I have?

Answer 3

(g*f)(-5) = g(-5)*f(-5)
f(-5) = (-5)^2+7 = 32
g(-5) = -5 - 3/5 = -28/5
g(-5)*f(-5) = -32*28/5
= -32*4*7/5
= -128*7/5
= -896/5
= -1792/10
= -179.2

Answer 4

Just to be clear, is that \(g *f\) or \(g\circ f\)?

Answer 5

The later, I'm pretty sure. I don't know the difference..

Answer 6

\(g *f\) means \(f(x)\cdot g(x)\) as in the functions are multiplied.
\(g\circ f\) means \(g[f(x)]\) as in the functions are composed.

Answer 7

If you are studying function composition, then you need to put f inside g to replace x. Once you have that, then you put the -5 inside the new function and find the answer.

Answer 8

I don't know how to do that, but thank you for explaining it.

Answer 9

Well, lets clarify one other thing first...
\( g(x)=x+3/x\) Hmmm. Did you mean:

\( g(x)=x+\dfrac{3}{x}\)
or
\( g(x)=\dfrac{x+3}{x}\)

Answer 10

The second one.

Answer 11

OK.

\(g(x)=\dfrac{x+3}{x}\)

Every place there is an x there, replace it with this: \((x^2+7)\)

Answer 12

\(g(x)=\dfrac{x+3}{x}\) becomes \(g(x)=\dfrac{(x^2+7)+3}{(x^2+7)}\)

Now, you can simplify it at that point if you needed the formula. Because you have a value to test, you could replace x with (-5) and just do the math at that point.

Answer 13

Well, techically

\(g(f(x))=\dfrac{(x^2+7)+3}{(x^2+7)}\)

^^^^^^ See how the f is inside the g at that point? That is the composition part.

Answer 14

Yeah, I do!

Answer 15

That is what makes the right side come out the way it does. Because I put the right side of f(x) inside the right side of g(x).

Now that it is in that form, put the (-5) in there, do the math, and you are done.

Answer 16

Okay! Can you help me with one or so more problems?

Answer 17

Not at the moment. Handling some reports. But it looks like a lot of helpers are on. =)

Answer 18

Okay, thank you anyway!

Answer 19

@sks23cu and that was nice. But I find it is best to be sure you know what the person is asking. Sometimes people make small mistakes typing stuff in, or don't know how to use the equation editor, so by confirming I can be sure I answer the right thing.

Answer 20

@sks23cu Can you perhaps help with my other questions? I'd make a new one so I could give you a best response and all.

Answer 21

I really appreciate your help.