IKMC 2027 - Grades 11-12 - Self-study SET 3 - Thematic Batch 3 Question 11

Question 11

Let f (x)=sin (cos x) and g (x)=cos (sin x), defined on[0, π/2]. Which assertion below is true?



Editorial note: More than one printed assertion is true; select all correct choices.

1. Equation f (x)=g (x) has exactly one solution
2. Equation f (x)=g (x) has infinitely many solutions
3. Equation f (x)=g (x) has no solution
4. f (x) $\lt$ g (x) for every x in the domain
5. f (x) > g (x) for every x in the domain