Question

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

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

Answer 1

\[f\circ g(x)\]?

Answer 2

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

Answer 3

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
\[4\times \frac{5}{x+6}-6\]

Answer 4

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

Answer 5

hmm, it says that isn't right

Answer 6

well maybe they want to you actually subtract

Answer 7

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

Answer 8

that's it! thank you :-)