# (F*g)(x) (G*f)(x)For calculus we are doing review and these have stumped me, I understand how to do fog and gof and such but I'm not sure what to do with equations like (fog)(x) I keep getting...

(F*g)(x) (G*f)(x)

For calculus we are doing review and these have stumped me, I understand how to do fog and gof and such but I'm not sure what to do with equations like (fog)(x) I keep getting extremely bizarre answers that are wrong(I checked). If someone could help me with one or two I can do the rest. Thank you so much!

f(x) = x + (1/x)

g(x) = (x + 14)/(x + 2)

(f*g)(x)=

domain =

(g*f)(x)=

domain=

(f *f)(x)=

domain=

(g*g)(x)=

domain=

*print*Print*list*Cite

### 1 Answer

With more than one question you need to make separate posts.

For the function `(f circ g)(x)`

this is the same as writing

`f(g(x))` substitute the definition of g into f

`=f({x+14}/{x+2})`

`={x+14}/{x+2}+1/{{x+14}/{x+2}}` now simplify

`={x+14}/{x+2}+{x+2}/{x+14}` get common denominators

`={(x+14)^2+(x+2)^2}/{(x+2)(x+14)}` simplify the numerator

`={x^2+28x+196+x^2+4x+4}/{(x+2)(x+14)}`

`={2x^2+32x+200}/{(x+2)(x+14)}`

`={2(x^2+16x+25)}/{(x+2)(x+14)}`

The domain of the function is all real numbers except the zeros of the denominator of the composite function and the zeros of the denominator of the argument.

**That means the domain is `{x in R|x ne -2, -14}` .**

**The composite function is `(f circ g) (x)={2(x^2+16x+25)}/{(x+2)(x+14)}` .**