THIS USER ASKED 👇

Which of the following is an odd function?

f(x) = x3 + 5×2 + x
f (x) = StartRoot x EndRoot
f(x) = x2 + x
f(x) = –x

THIS IS THE BEST ANSWER 👇

f (x) = - x

Step by step explanation:

When f (-x) = -f (x), it is then called 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

ie f (-x)  neq-f (x)

ii) f (x) =  sqrt {x}

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

ie f (-x)  neq-f (x)

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

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

ie f (-x)  neq-f (x)

iv) f (x) = - x

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

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

ie f (-x) = - f (x)

Hence, f (x) is an odd function.