Question

If $f\left(x\right)=\log x$ and $g\left(x\right)=x^3$ find $fog\left(a\right)+fog\left(b\right)$.

Answer 1

Given, $g\left(x\right)=x^3$ and $f\left(x\right)=\log x$

$f\left[g\right(x\left)\right]=\log \left(g\right(x\left)\right)\Rightarrow fog=\log x^3=3\log x$

Thus $fog\left(a\right)+fog\left(b\right)=3\log a+3\log b$

$\Rightarrow fog\left(a\right)+fog\left(b\right)=3(\log a+\log b)\Rightarrow fog\left(a\right)+fog\left(b\right)=3\log ab\Rightarrow fog\left(a\right)+fog\left(b\right)=\log {\left(ab\right)}^3$