(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If [tex]\lim_{x\rightarrow 0+}f(x)=A [/tex]

and

[tex]\lim_{x\rightarrow 0-}f(x)=B[/tex] find

[tex]\lim_{x\rightarrow 0+}f(x^{3}-x)[/tex]

2. Relevant equations

3. The attempt at a solution

I dont have one. Im dumbfounded. Mostly i have been trying to understand the meaning of the composite function. Im not sure if this is correct but

[tex]f(x^{3}-x) =f(x(x^{2}-1))= f(x)f(x^{2}-1)[/tex]

Then i have at least isolated f(x), whose limit is known, but the other factor i dont know what to do about.

I've been thinking about the meaning of the limits for the original function f(x). Since A is not equal to B, f(x) is not even. f(x) could be odd, but we dont know that. I dont know how that would help me, its just something i thought of.

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# Right limit of a composite function. Original functions limits are known.

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