Which of the following functions is an injective (one-one) function in its respective domain? (A) `f(x) = 2x + sin 3x ` (B) `x. [x]` , (where `[.]` denotes the G.I.F) (C) `f(x)=(2^x-1)/(4^x+1)` (D) `f(x)=(2^x+1)/(4^x-1)`

Find Domain of the following function : f(x)=sin^(-1)[2x^2-3] , where [.] devotes G.I.F.

The domain of f(x)=sin^(-1)[2-4x^(2)] (where [.] is G.I.F) is

If f(x) is a real valued function, then which of the following is injective function ? (i) f(x) = x^(5) (ii) f(x) = x + sin x (iii) f(x) = x^(2) (iv) f(x) = e^(x) (v) f(x) = x^(3) + x^(2) + 4x + 4

If f(x) is a real valued function, then which of the following is injective function ? (i) f(x) = x^(5) (ii) f(x) = x + sin x (iii) f(x) = x^(2) (iv) f(x) = e^(x) (v) f(x) = x^(3) + x^(2) + 4x + 4

Discuss the continuity of f(x) in [0,2] where f(x) = {{:([cos pi x]" , " x le 1),(| 2x - 3 |.[ x- 2]" ," x gt 1):} where [.] denotes the G.I.F.

If domain of f(x) is [-1,2] then domain of f(x]-x^(2)+4) where [.] denotes the greatest integer function is

If domain of y=f(x) is [-4,3], then domain of g(x)=f(|x]|) is,where [.] denotes greatest integer function

Which of the following function is/are periodic? A. f(x)={1,0,x is rationalx is irrational B. f(x)={x−[x],12,2n≤x<2n+12n+1≤x<2n+2 where [.] denotes the greatest integer function n∈Z C. f(x)=(−1)[2xπ, where [.] denotes the greatest integer function D. f(x)=x−[x+3]+tan(πx2), where [.] denotes the greatest integer function, and a is a rational number

Which of the following function(s) is/are transcendental? a. f(x)=5sin(sqrt(x)) b. f(x)=(2sin3x)/(x^(2)+2x-1) c. f(x)=sqrt(x^(2)+2x+1) d. f(x)=(x^(2)+3)*2^(x)

Let f:(2,4)->(1,3) where f(x) = x-[x/2] (where [.] denotes the greatest integer function).Then f^-1 (x) is