Question

Which of the following is an odd function?

Answer 1

Answer: $f(x)=-x$

Step-by-step explanation:

When f(-x)= -f(x), then it is known as an odd function.

i) $f(x) = x^3 + 5x^2 + x$

Then, $f(-x)=(-x)^3+5(-x)^2+(-x)=-x^3+5x^2-x\neq -x^3-5x^2-x$

i.e. $f(-x)\neq-f(x)$

ii) $f(x)=\sqrt{x}$

$f(-x)=\sqrt{-x}\neq-\sqrt{x}$

i.e. $f(-x)\neq-f(x)$

iii) $f(x)=x^2+x$

$f(-x)=(-x)^2+(-x)=x^2-x\neq-x^2-x$

i.e. $f(-x)\neq-f(x)$

iv) $f(x)=-x$

$f(-x)=-(-x)=x$

$-f(x)=-(-x)=x$

i.e. $f(-x)=-f(x)$

Hence, f(x) is an odd function.

Answer 2

Answer:

i think its d on edge i may be wrong

Step-by-step explanation: