Find (f*g)(x) for the indicated functions:

f(x)=4x-6, g(x)= 5/x+6

Question

Find (f*g)(x) for the indicated functions:

f(x)=4x-6, g(x)= 5/x+6

anonymous · Answer

$$f\circ g(x)$$?

anonymous · Answer

yes, sorry I  don't know how to make the little circle thing

anonymous · Answer

first write 
$$f(g(x))$$ then replace g by what it is 
$$f(\frac{5}{x+6})$$ then replace the x in f(x) by the new input to get 
$$4\times \frac{5}{x+6}-6$$

anonymous · Answer

and you can write 
$$f\circ g(x)=\frac{20}{x+6}-6$$ but nothing cancels so you should be done at this step

anonymous · Answer

hmm, it says that isn't right

anonymous · Answer

well maybe they want to you actually subtract

anonymous · Answer

$$\frac{20}{x+6}-6=\frac{20}{x+6}-\frac{6(x+6)}{x+6}$$
$$=\frac{20-(6x+36)}{x+6}$$
$$=\frac{-6x-16}{x+6}$$ but that seems like a lot of extra work to me

anonymous · Answer

that's it! thank you :-)