Question

Consider the function h as defined. Find functions f and g so
(f o g)(x)=h(x)
h(x)=8/x^2+10

I think it is:

h(x)=8/x^2+10
h(x)=8/x^2+10*x^2/x^2
h(x)=8/x^2+10x^2/x^2
h(x)=8+10x^2/x^2
h(x)=10x^2+8/x^2
h(x)=2(5x^2)+2(4)/x^2
h(x)=2(5x^2+4)/x^2

Answer 1

say g(x) = 1/x
f(g) = 8/g^2= = 8/x^2
H(f) = g+10 = 8/x^2 + 10
then
g(x) = 1/x
f(x) = 8/[g(x)]^2
h(x) = f(x) + 10