Question

R 8. If f:R → R defined by f(x) = 4 R 1+ 3x2 -cos 2x -, for x = 0 is continuous x=0, then k= [ k x2 ,x=0 1) 1 2) 5 3) 6 4) o (2 sin x-sin 2x​

Answer 1

Solution

Correct option is

C

[ 43

,1]y=f(x)=cos 2

x+sin

4

x

⇒y=f(x)=cos

2

x+sin

2

x(1−cos

2

x)

⇒y=cos

2

x+sin

2

x−sin

2

xcos

2

x

⇒y=1−sin

2

xcos

2

x

⇒y=1−

4

1

sin

2

2x

∴

4

3

≤f(x)≤1

⇒f(x)ϵ[3/4,1]