Question

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

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

Answer 1

The correct option is B $f\left[g\right(ab\left)\right]$

Given that $g\left(x\right)=x^3$. Therefore,

$f\left[g\right(a\left)\right]+f\left[g\right(b\left)\right]=f\left(a^3\right)+f\left(b^3\right)$.

Since $f\left(x\right)=\log x$, we have

$f\left(a^3\right)+f{b}^3=\log a^3+\log b^3$

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

$=f\left[g\right(ab\left)\right]$