SOLUTION: Find functions f and g such that h = f ◦ g h(x) = sin (x^2+1)

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Question 596299: Find functions f and g such that h = f ◦ g
h(x) = sin (x^2+1)
Found 2 solutions by richard1234, math-vortex:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Let g be the inner function, that is:

g(x) = x^2 + 1
f(x) = sin x

Then f(g(x)) = sin (x^2 + 1)

Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Find functions f and g such that h = f ◦ g
h(x) = sin (x^2+1).
Hi, there-
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In your problem, h(x)=f(g(x)) is a composite function. So f(x) = sin(x) and g(x) = x^2 + 1. Here's why:
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The composite function h(x) is asking you to notice patterns and to figure out what is "inside" something else. In this case, h(x) looks similar to the sine function, except that, instead of sin(x), We are finding the sine of x^2+1.
In other words, this is a sine function into which we've plugged x^2 + 1. So we make g(x) = x^2 + 1, and then plug this function into f(x) = sin(x).
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That's it. Feel free to email if you still have questions about this.
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Ms.Figgy
math.in.the.vortex@gmail.com