Question

If f(x) = x3 - 3x + sin x, find f(x) + f(-x) =?​

Answer 1

Answer:

f(x)=x3+x2+3x+sinx.

⇒f′(x)=3x2+2x+3+cosx≥3x2+2x+3−1, since −1≤cosx≤1

⇒f′(x)≥3x2+2x+2

Now discriminant of above quadratic is =22−4⋅3⋅2<0

Hence f′(x)>0 for all x∈R

Therefore f is one-one function, also every odd degree polynomial

has it's range R. Thus f is an onto function

Step-by-step explanation: