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April 24th, 2014, 02:19 PM   #1
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f(x)

f(x^2 +1)=x^4 +2x^2+1
find domain and rang of
f
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April 24th, 2014, 03:46 PM   #2
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It looks like f(x) = x^2.

I am not sure what you want.
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April 24th, 2014, 05:11 PM   #3
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Well the domain would be $[1,+\infty)$ I suppose. The range would be the corresponding values of $f(x^2 + 1)$.
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April 24th, 2014, 10:20 PM   #4
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The function is $f(g(x))=x^4+2x^2+1$ where $g(x)=x^2+1$ and $f(x)=x^2$ so the domain and range are both $[1,\,\infty)$.
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April 24th, 2014, 10:44 PM   #5
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I think the domain is (-infinity. +infinity) because x can take any value
and range is [1, +infinity)
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April 24th, 2014, 10:49 PM   #6
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Quote:
Originally Posted by rickkkyrich View Post
I think the domain is (-infinity. +infinity) because x can take any value
Nope. $(-\infty,\,\infty)$ is the domain of $g(x)$. The domain of $f(g(x))$ is the range of $g(x)$, namely $[1,\,\infty)$.
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April 24th, 2014, 11:03 PM   #7
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Yes you are right. Thanks for correcting
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