Question

If $f\left(x\right)=4x-3$ and $g\left(x\right)=x-4$, determine which of the following composite function has a value of $-11$.

• A. $f\left(g\right(2\left)\right)$
• B. $g\left(f\right(2\left)\right)$
• C. $g\left(f\right(3\left)\right)$
• D. $f\left(g\right(3\left)\right)$
• E. $f\left(g\right(4\left)\right)$

Answer 1

The correct option is A $f\left(g\right(2\left)\right)$

Given, $f\left(x\right)=4x-3,g\left(x\right)=x-4$

$\Rightarrow f\left(g\right(2\left)\right)=f(-2)=-11$
$\Rightarrow g\left(f\right(2\left)\right)=g\left(5\right)=1$
$\Rightarrow g\left(f\right(3\left)\right)=g\left(9\right)=5$
$\Rightarrow f\left(g\right(3\left)\right)=f(-1)=-7$
$\Rightarrow f\left(g\right(4\left)\right)=f\left(0\right)=-3$