Let `f: RvecR` be such that `f(x)=2^x` . Determine: Range of `f` (ii) `{x :f(x)=1}` (iii) Whether `f(x+y)=f(x)f(y)` holds.

Let f:RtoR:f(x)=x^(2) . Determine (i) range (f) (ii) {x:f(x)=4}

If f:R rarr R is a function such that f(x)=2^(x), find.(i) range of f( ii) (x:f(x)=1) (iii) f(x+y)=f(x)+f(y) is true or false.

Let f: R->R whre R^+ is the set of all positive real numbers, be such that f(x)=(log)_e xdot Determine: whether f(x y)=f(x)+f(y) holds.

Let f:RtoR be defined by f(x)=x/(1+x^2),x inR . Then the range of f is

Let f(x)=(1)/(1+|x|) ; x in R the range of f is

Let f:R to R such that f(x+y)+f(x-y)=2f(x)f(y) for all x,y in R . Then,

Let f : R to R be a function such that f(0)=1 and for any x,y in R, f(xy+1)=f(x)f(y)-f(y)-x+2. Then f is

If f(x)=cos(log x), then f(x)f(y)-(1)/(2)[f((x)/(y))+f(xy)]=

If f(x)=cos(log x), then f(x)f(y)-(1)/(2)[f((x)/(y))+f(xy)]=

Let f : R to R be a function such that f(x+y) = f(x)+f(y),Aax, y in R. If f (x) is differentiable at x = 0, then