Math Help - Basic 'Logs' and 'Functions'

1. Basic 'Logs' and 'Functions'

Hi guys,

Just wondering if anyone would be able to help me on this specific questions?

All of question 12

Cheers guys really appreciate it!!

2. Any ideas guys?

3. Are you sure you're not supposed to evaluate $\displaystyle fg(x)$? If so, $\displaystyle fg(x) = f(x)\cdot g(x)$.

4. Originally Posted by Prove It
Are you sure you're not supposed to evaluate $\displaystyle fg(x)$? If so, $\displaystyle fg(x) = f(x)\cdot g(x)$.
That's what I thought initially, however the answer in the back of the book is simply: "2". Spark any mathematical ideas of yours?

5. OK, you will first need to get a function $\displaystyle fg(x)$ and then evaluate it at $\displaystyle x=k$.

6. Actually, you don't need to find fg(x). fg(x)= f(x)g(x) and g(k)= ?

HOWEVER, if the answer in the book is "2", they mean $f\circ g(k)$, the composition, NOT $fg(k)$, the product. I'm very surprised a textbook would make that error. But, again, you do not need to find $f\circ g(x)$, just find g(k) and then f of that value.

$f^{-1}(x)$ is easy- but you will need a logarithm.