Question

h(x)=5/x^2+6
I know the answer is: f(x)=x+6, g(x)=5/x^2, but I do not know how to get it. Can someone help me understand it?

Answer 1

First break it down
x=x+6 and x=5/x^2
x=-1 x=2.5

Answer 2

You did not state the question.
Is it
h of f of g of x = 5/x^2 + 6 ?

There is surely more than one answer you can find by trial and error. For example another might be:
try g(x) = 1/x^2
then f(x) = 5 x
then f (g) = 5 (1/x^2) = 5/x^2 which is what I want except I have to add 6
so say h(x) = x + 6
then h (f) = 5/x^2 + 6
so the sequence
g(x) = 1/x^2
f(x) = 5 x
h(x) =x + 6
also yields
h(x) = 5/x^2 + 6

Answer 3

Consider the function h as defined. Find functions f and g so that
(f o g)(x)=h(x)

h(x)=5/x^2+6

Answer 4

oh
then I would modify that answer:

There is surely more than one answer you can find by trial and error. For example another might be:
try g(x) = 1/x^2
then f(x) = 5 x + 6
then f (g) = 5 (1/x^2) +6 = 5/x^2 + 6
then h (f) = 5/x^2 + 6
so the sequence
g(x) = 1/x^2
f(x) = 5 x + 6
also yields
h(x) = 5/x^2 + 6