Question

Determine whether the function
fz- log2^x^2
is even as odd function​

Answer 1

Answer:

f(x)=log(2−x2+x)f(x)=log⁡(2−x2+x)

Check f(−x)f(−x) to identify whether f(x)f(x) is even or odd function

f(−x)=log(2+x2−x)f(−x)=log⁡(2+x2−x)

⟹f(−x)=log(2−x2+x)−1⟹f(−x)=log⁡(2−x2+x)−1

We know that logmn=nlogmlog⁡mn=nlog⁡m

⟹f(−x)=−log(2−x2+x)⟹f(−x)=−log⁡(2−x2+x)

⟹f(−x)=−f(x)⟹f(−x)=−f(x)

Hence ff is an odd function.

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