Question

Let f(x)=x-cos⁡x,x∈R, then f is​

Answer 1

Given :  f(x)=x-cos,x€R

To find :  f is:

O A. a decreasing fonction

O B. an increasing function

O C. an odd function

O D. none of these​

Solution:

f(x) = x  - cosx

f(-x)  = -x - cos(-x)

=> f(-x) = - x - cosx

f(x) ≠ f(-x)

f(x) ≠ - f(-x)

neither odd nor even function

f(x) = x  - cosx

=> f'(x) = 1  +  sinx

f'(x) = 1+  sinx

-1 ≤sinx)  ≤ 1

0  ≤ f(x) ≤ 2

0  ≤ f(x)

Hence f(x) is  a  increasing function

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