Which of the following is an odd function?
f(x) = x3 + 5x2 + x
o f(x)= √x
of(x) = x2 + x
o f(x) = -x

Option 4

f(x) = -x is an odd function

Solution:

A function is odd if and only if f(–x) = –f(x)

Option 1

Substitute x = -x in above equation

Cubes always involve multiplying a number by itself three times, so if the number is negative the cube will always be negative

Ans squaring results in positive

 --- eqn 1

 ---- eqn 2

Comparing eqn 1 and eqn 2,

Therefore not an odd function

Option 2

Therefore,

Therefore not an odd function

Option 3

Therefore not an odd function

Option 4

Thus option 4 is correct and it is an odd function

d

step-by-step explanation:

5

step-by-step explanation: