Question

If h(x)=(fog)(x) and h(x)=5(x+1)^3, find f(x) and g(x)

a. f(x)=5x^3, g(x)=(x+1)^3
b. f(x)=(x+1)^3, g(x)=5x^3
c. f(x)=x+1, g(x)=5x^3
d. f(x)=5x^3, g(x)=x+1

Would it be d.

Please help and explain!

Answer 1

\[\Large\rm g(x)=x+1\]\[\Large\rm f(\color{royalblue}{x})=5(\color{royalblue}{x})^3\]So plugging g(x) into f,\[\Large\rm f(\color{royalblue}{g(x)})=5(\color{royalblue}{g(x)})^3\]\[\Large\rm f(\color{royalblue}{g(x)})=5(\color{royalblue}{x+1})^3\]Mmm yah that seems to work out! :)

Answer 2

So D then?