CAT 2019 Functions Question (Hard)

Question

The number of the real roots of the equation 2cos x x 1 2 x 2 -x is

Accepted Answer

Step 1 Given equation 2 cos x x 1 2x 2 x x 2 So the equation becomes 2 cos x x x 2 Step 2 Range of LHS Since 1 cos any real 1 2 cos x x lies in 2, 2 So RHS must also lie within 2, 2 i.e., x 2 2, 2 x 4, 0 Step 3 Let f x 2 cos x x Let g x x 2 Graphically, f x is a cosine function g x is a straight lin

CAT 2019

Quantitative

Functions

Hard

The number of the real roots of the equation 2cos(x(x + 1)) = 2 x + 2 -x is

Transform Your Interview Performance!

Practice

Features

Support