Posted by **Tim** on Saturday, March 29, 2008 at 4:41pm.

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?

- Algebra -
**Anonymous**, Saturday, March 29, 2008 at 5:42pm
First break it down

x=x+6 and x=5/x^2

x=-1 x=2.5

- Algebra -
**Damon**, Saturday, March 29, 2008 at 6:03pm
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

- Algebra -
**TIm**, Saturday, March 29, 2008 at 6:07pm
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

- Algebra -
**Damon**, Saturday, March 29, 2008 at 6:32pm
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

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