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Identify the following functions : f(x)=...

Identify the following functions : `f(x)=xg(x)g(-x)+"tan"(sinx)`

A

Odd

B

Even

C

Neither

D

Both

Text Solution

Verified by Experts

The correct Answer is:
A
`f(-x)=(-x)g(-x)*g(x)+tan(sin(-x))`
`= -(xg(x)g(-x)+tan(sinx))= -f(x)`
Hence, `f(x)` is an odd function.
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CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Identify the type of the functions: f(x)={g(x)-g(-x)}^(3)

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  2. Identify the following functions whether odd or even or neither: f(x)=...

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  3. Identify the following functions : f(x)=xg(x)g(-x)+"tan"(sinx)

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  4. Identify the following functions: f(x)=cos["x"]+[(sinx)/2] where [dot...

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