Question

If $f\left(x\right)=\log x$, $g\left(x\right)=x^3$, then $f\left[g\right(a\left)\right]+f\left[g\right(b\left)\right]$ equals

• A. $f\left[g\right(a)+g(b\left)\right]$
• B. $3f\left(ab\right)$
• C. $g\left[f\right(ab\left)\right]$
• D. $g\left[f\right(a)+f(b\left)\right]$

Answer 1

Answer: (B)

$3f\left(ab\right)$

We have $f\left(x\right)=\log x$

$g\left(x\right)=x^3$

$g\left(a\right)=a^3$

$f\left(g\right(a\left)\right)=\log \left(a^3\right)$

$f\left(g\right(a\left)\right)=3\log a$

Similarly,

$f\left(g\right(b\left)\right)=3\log b$

$\Rightarrow f\left(g\right(a\left)\right)+f\left(g\right(b\left)\right)=3\log a+3\log b$

$\Rightarrow f\left(g\right(a\left)\right)+f\left(g\right(b\left)\right)=3\log ab$

$\Rightarrow f\left(g\right(a\left)\right)+f\left(g\right(b\left)\right)=3f\left(ab\right)$