Question

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

• A. 5/3
• B. 3/2
• C. 2/3
• D. 3/5

Answer 1

Answer: (B)

3/2

$\left(fog\right)\left(x\right)=f\left(g\right(x\left)\right)=2(3x-5)+1=6x-10+1=6x-9$
Let $\left(fog\right)\left(x\right)=y$
Then, to find $\left(fog{)}^{-1}\right(x)$, we find $x$ in terms of $y$
So, $6x-9=y$
$=>x=\frac{y+9}{6}$
$=>\left(fog{)}^{-1}\right(x)=\frac{y+9}{6}$
$=>\left(fog{)}^{-1}\right(0)=\frac{0+9}{6}=\frac{3}{2}$