I have answer can't figure how to get there

[kdtup]

Find formula for function and simplify f(x)=(x^2)+1, g(x) =1/x-3, h(x) =sq root of x

The problem is f(g(x))

the answer is: (x^2-6x+10) / (x^2-6x+9)[/img][/quote][/list]

 

[daon]

I find it students understand this more when there are less parentheses, so... Lets say u = g(x) = $\displaystyle \frac{1}{x-3}$. You want to find f(u).

If f(x) = $\displaystyle x^2+1$, then f(u) = $\displaystyle u^2+1$

But what is u? u = $\displaystyle \frac{1}{x-3}$, so, f(u) = $\displaystyle (\frac{1}{x-3})^2 + 1$.

Simplifying,

$\displaystyle (\frac{1}{x^2 - 6x + 9}) + 1$ = $\displaystyle (\frac{1}{x^2 - 6x + 9}) + \frac{x^2 - 6x + 9}{x^2 - 6x + 9}$

Finally,


f(u) = f(g(x)) = \(\displaystyle \L\\ \frac{x^2-6x+10}{x^2 - 6x + 9}\)