Question

If $f\left(x\right)=$ $x^2$ and $g\left(x\right)=2x$, calculate the value of $f\left(g\right(-3\left)\right)-g\left(f\right(-3\left)\right)$.

• A. 54
• B. 18
• C. 0
• D. -18
• E. -54

Answer 1

The correct option is B 18

Given $f\left(x\right)=x^2$ and $g\left(x\right)=2x$.

Then $f(-3)={(-3)}^2=9$ and $g(-3)=2(-3)=-6$

So, $f\left(g\right(-3\left)\right)=\left[g\right(-3){]}^2={[-6]}^2=36$

and $g\left(f\right(-3\left)\right)=2\ast f(-3)=2\ast 9=18$

The value of $f\left(g\right(-3\left)\right)-g\left(f\right(-3\left)\right)$ is $36-18=18$