JEE Advanced Model Paper 14 with solutions for online practice

f (x) = √2 sin (

π

4

+x)
Suppose for a natural number k, f(x) assumes values √2 sin (

π

4

+x) then the same value is assumed
again by the function at P = nπ + (−1)p (

π

4

+k)
Irrespective of‘n’ P can never be a natural number.
Hence f(x) is one-one.
Further f(x) cannot attain all values in [-√2 , √2] which √2 sin (

π

4

+x) attains irrational values.
e.g. f (x) = 0 when

π

4

+ x = nπ which is not true for x ∊ N. -Hence into.