Question

If $f\left(x\right)=2x+1$ and $g\left(x\right)=3x-5$, then find $\left(fog{)}^{-1}\right(0)$.

• A. $\frac{5}{3}$
• B. $\frac{3}{2}$
• C. $\frac{2}{3}$
• D. $\frac{3}{5}$
  

Answer 1

The correct option is B $\frac{3}{2}$

$fog\left(x\right)=2(3x-5)+1=6x-10+1=6x-9$

Let $fog$ be $y$

$y=6x-9$

$\Rightarrow x=\frac{y+9}{6}$

Hence $\left(fog{)}^{-1}\right(x)=\frac{x+9}{6}$

So $\left(fog{)}^{-1}\right(0)=\frac{9}{6}=\frac{3}{2}$