Answer:
(gof) (4) = 9
Hence, option A is true.
Step-by-step explanation:
f(x)=-x³
g(x)=|1/8x -1|
(gof) (4) = g{f(4)}
First wee need to determine f(4)
f(4)=-(4)³
= -64
so
(gof) (4) = g{f(4)} = g(-64)
= [tex]\left|\frac{1}{8}\left(-64\right)-1\right|[/tex]
[tex]=\left|-\frac{1}{8}\cdot \:64-1\right|[/tex]
[tex]=\left|-8-1\right|[/tex]
[tex]=\left|-9\right|[/tex]
[tex]\mathrm{Apply\:absolute\:rule}:\quad \left|-a\right|=a[/tex]
[tex]=9[/tex]
Thus,
(gof) (4) = 9
Hence, option A is true.
