Question

Which of the following functions even and which are odd?
(i) $f\left(x\right)=x^2+7$
(ii) $f\left(x\right)=x+2$
(ii) $f\left(x\right)=x^7+2x^5$
(iv) $f\left(x\right)=\left|x\right|+4$

Answer 1

$\left(i\right)f\left(x\right)=x^2+7$
$f\left(x\right)=f(-x)$
$\Rightarrow even$

(ii) $f\left(x\right)=x+2$

$f(-x)=-x+2$

$=-(x-2)$

$f\left(x\right)\ne f(-x)$

Neither even nor odd

(iii)$f\left(x\right)=x^7-2x^5$

$f(-x)=-x^7-2x^5$

$=-(x^7+2x^5)$

$f(-x)=-f\left(x\right)$

$\Rightarrow odd$

(iv)$f\left(x\right)=|x|+4$

$f(-x)=|-x|+4$

$=|x|+4$

$f\left(x\right)=f(-x)$

$\Rightarrow even$