Question

If f(x)=x3+ 3 sinx + x then show
that f(x) is
an odd
function
​

Answer 1

Answer:

if f(-x)=-f(x) so this will be odd function...

Answer 2

If a function f(x) is odd-function, f(-x) = - f(x)

If a function f(x) is even-function, f(-x) = f(x)

  In the question,

f(x) = x³ + 3sinx + x

∴  f(-x) = (-x)³ + 3sin(-x) + (-x)

           = -x³ + 3(-sinx) - x

           = - x³ - 3sinx - x

           = - (x³ + 3sinx + x)

           = - f(x)

As f(-x) = - f(x),  this is an odd function.

Note that: sin(-x) = - sinx