Let `f: R->R and g: R->R` be two given functions such that `f` is injective and `g` is surjective. Then which of the following is injective? (a)`gof` (b) `fog` (c) `gog` (d) none of these

Let f:R->R and g:R->R be two one-one and onto functions such that they are mirror images of each other about the line y=a . If h(x)=f(x)+g(x) , then h(x) is (A) one-one onto (B) one-one into (D) many-one into (C) many-one onto

Let R be the set of real numbers. If f:R->R is a function defined by f(x)=x^2, then f is (a) injective but not surjective (b) surjective but not injective (c) bijective (d) none of these

Let f: R->R be a function such that f(x)=a x+3sinx+4cosxdot Then f(x) is invertible if (a) a in (-5,5) (b) a in (-oo,5) (c) a in (-5,+oo) (d) none of these

Let f:R->R be a continuous function such that |f(x)-f(y)|>=|x-y| for all x,y in R ,then f(x) will be

Let f:R to R and h:R to R be differentiable functions such that f(x)=x^(3)+3x+2,g(f(x))=x and h(g(x))=x for all x in R . Then,

Let f: R->R and g: R->R be two non-constant differentiable functions. If f^(prime)(x)=(e^((f(x)-g(x))))g^(prime)(x) for all x in R , and f(1)=g(2)=1 , then which of the following statement(s) is (are) TRUE? f(2) 1-(log)_e2 (c) g(1)>1-(log)_e2 (d) g(1)<1-(log)_e2

In any triangle, the minimum value of r_1r_2r_3//r^3 is equal to 1 (b) 9 (c) 27 (d) none of these

The function f: NvecN(N is the set of natural numbers) defined by f(n)=2n+3i s (a) surjective only (b) injective only (c) bijective (d) none of these

Let f: A to B and g: B to C be two functions. Then; if gof is onto then g is onto; if gof is one one then f is one-one and if gof is onto and g is one one then f is onto and if gof is one one and f is onto then g is one one.

Let f and g be two functions from R to Rdefined by f(x) = 3x – 2 and g(x) = x^(2)+3 . Then gcircf is: