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  • If is an even function and  is an odd function, then  <img alt="h(x)=f(x) \cdot g(x)" s

If f(x) is an even function and g(x) is an odd function, then  h(x)=f(x) \cdot g(x)  is
 

Option: 1

 Even function
 


Option: 2

Odd function
 


Option: 3

Neither even nor odd
 


Option: 4

Can't tell


Answers (1)

best_answer

          \begin{aligned} h(x)=& f(x) \cdot g(x) \\ \end{aligned}

So,    \begin{aligned} h(-x)=& f(-x) \cdot g(-x) \end{aligned}

                        \begin{aligned} \\ =& f(x) \cdot(-g(x)) \end{aligned}
\begin{aligned} &\{\text { As } f(x) \text { is even } \Rightarrow f(-x)=f(x) \text { and }\\ &g(x) \text { is odd } \Rightarrow g(-x)=-g(x)\} \\ \end{aligned}

                        \begin{aligned} &=-f(x) \cdot g(x) \\ &=-h(x) \\ \end{aligned}

\begin{aligned} \Rightarrow \quad h(-x) &=-h(x) \end{aligned}
So  h (x)  is an odd function.

Posted by

vishal kumar

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