Question

H(x)=(g o f)(x)=1/(x+3)^2 which of the fallowing could be a possible decomposition of h(x)? A. f(x)=1/x^2;g(x)=x+3 B. f(x)=x+3; g(x)=1/x^2 C.f(x)=x^2; g(x)=x+3 D. f(x)=1/x;g(x)=x+3

...?

Answer 1

f(x)=x+3; g(x)=1/x^2

If you take B f(x)=x+3 g(x)=1/x^2 plug the f(x) into the g(x) formula (in other words, f(x) becomes the x for g) g(x)=1/x^2 g(x)=1/(x+3)^2

Answer 2

I am pretty sure that the only possibl decomposition of the finction represented above is being revealed by the second option - B. f(x)=x+3; g(x)=1/x^2. I choose this one because I plugged the f(x) into the g(x) and that's what I got :
`g(x)=1/x^2 g(x)=1/(x+3)^2`