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Identify the type of the functions: f(x)...

Identify the type of the functions: `f(x)={g(x)-g(-x)}^(3)`

A

Odd

B

Even

C

Neither

D

Both

Text Solution

Verified by Experts

The correct Answer is:
A
`f(-x)=(g(-x)-g(x))^(3)= -(g(x)-g(-x))^(3)= -f(x)`
Hence, `f(x)` is an odd function.
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Knowledge Check

  • Let g(x) be the inverse of the function f(x) and f'(x)=(1)/(1+x^(3)) , then g'(x) is equal to

    A
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    C
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  • Let g be the greatest integer function. Then the function f(x)=(g(x))^(2)-g(x) is discontinuous at

    A
    all integers
    B
    all integers except 0 and 1
    C
    all integers except 0
    D
    all integers except 1

  • Suppose f, g, and h be three real valued function defined on R. Let f(x) = 2x + |x|, g(x) = (1)/(3)(2x-|x|) and h(x) = f(g(x)) The domain of definition of the function l (x) = sin^(-1) ( f(x) - g (x) ) is equal to

    A
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    B
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