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4 votes
Find

f ∘ g ∘ h.

f(x) = (1)/(x) , g(x) = x^3, h(x) = x^2 + 5

(just a little confused on what to do for composite fractions)

Find f ∘ g ∘ h. f(x) = (1)/(x) , g(x) = x^3, h(x) = x^2 + 5 (just a little confused-example-1

2 Answers

4 votes

Answer:

1/(x^2+5)^3 *

Explanation:

User Boanerges
by
8.0k points
4 votes

Answer:


\sf (f\circ g\circ h)(x) = (1)/( (x^2+5)^3)

Explanation:

Given:


\sf f(x) = (1)/(x)


\sf g(x) = x^3


\sf h(x) = x^2 + 5

To find:


\sf f\circ g \circ h

Definition:

Solution:

Given:


\sf f(x) = (1)/(x)


\sf g(x) = x^3


\sf h(x) = x^2 + 5

To find:


\sf f\circ g \circ h

Definition:

The composite function
\sf fcirc g\circ h is defined as follows:


\sf (f\circ g\circ h)(x) = f(g(h(x)))

In other words, to evaluate
\sf f\circ g\circ h at a point x, we first evaluate h(x), then substitute that result into g(x), and finally substitute the result of that into f(x).

Solution:

To find
\sf f\circ g \circ h, we simply substitute the functions $g(x)$ and $h(x)$ into the function $f(x)$ as follows:


\sf \begin{aligned} f\circ g\circ h(x) & = f(g(h(x))) \\\\ &= f(g(x^2+5))\\\\ &= f((x^2 + 5)^3 )\\\\ &= (1)/( (x^2+5)^3) \end{aligned}

Therefore,


\sf (f\circ g\circ h)(x) = (1)/( (x^2+5)^3)

User Gertjan Assies
by
8.1k points

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