Question

Which of the following is an odd function?

f(x) = x3 + 5x2 + x
f (x) = StartRoot x EndRoot
f(x) = x2 + x
f(x) = –x

Answer 1

D

Explanation:

if you don't want to read

Answer 2

Answer:
`f(x)=-x`

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\\eq -x^3-5x^2-x`

i.e.
`f(-x)\\eq-f(x)`

ii)
`f(x)=√(x)`

`f(-x)=√(-x)\\eq-√(x)`

i.e.
`f(-x)\\eq-f(x)`

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

`f(-x)=(-x)^2+(-x)=x^2-x\\eq-x^2-x`

i.e.
`f(-x)\\eq-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.