Discussion Forum

A function  $f:R-\left\{0\right\}\rightarrow R$ is defined as  

$f(x)=\begin{cases}x^{2}+3x-7, & x > 0\\h(x) ,& x < 0\end{cases}$

 If f(x)  is an odd function, then h(x)=

Answer:

Explanation:

$f(x)=\begin{cases}x^{2}+3x-7, & x > 0\\h(x) ,& x < 0\end{cases}$

 f(x)  is odd function, then h(x)=?

 forr odd function

 $h(-x)= -h(x) \Rightarrow   h(-x)= (-x)^{2}-3x-7$

$\Rightarrow$  $ h(-x)=x^{2}-3x-7$

$\Rightarrow$  $-h(x)=-[x^{2}-3x-7] \Rightarrow $   $-x^{2}+3x+7$