[Math] Expressing a function in terms of compositions of three functions.

algebra-precalculusfunctions

Express the function F in the form $f \circ g \circ h$.

$$F(x)=\frac {9}{( x^2 + 7)}$$

I'm not sure how to get $x^2+7$ in the denominator. Here is what I tried:

$$h(x) = (x+7)$$

$$g(x) = x$$

$$f(x) = \frac {9}{x^2}$$

But obviously that gives me $F(x) = \dfrac {9}{(x+7)^2}$ which isn't right… any help is appreciated!

Best Answer

Here’s what you do in general: suppose you want to compute a value of your function. What do you do, in order? Clearly you first square your value of $x$; then you add $7$; then you divide the result into $9$. Now traanslate each of these steps into functional notation, and you have it.

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