Question

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

• A. $-480$
• B. $-384$
• C. $0$
• D. $384$
• E. $480$

Answer 1

The correct option is A $-480$

• $f(-2)=2\times {(-2)}^3=-16$
• $g\left(2\right)=3\times 2=6$
• $g\left(f\right(-2\left)\right)=g(-16)=3\times -16=-48$
• $f\left(g\right(2\left)\right)=f\left(6\right)=2\times {\left(6\right)}^3=432$
• $g\left(f\right(-2\left)\right)-f\left(g\right(2\left)\right)=-48-432=-480$