Let `f,g:R->R` be two function difinite `f(x)={xsin(1/x), x!=0; and 0, x=0` ,and `g(x)=xf(x)`

Let f,g: RrarrR be two functions defined as f(x)=|x|+x and g(x)=|x|-xAAx in R . Then f(g) (x) for xlt0 is

Let f, g : R rarrR be two functions defined as f(x) = |x| + x and g(x) = | x| - x AA x in R. . Then (fog ) (x) for x lt 0 is

Let g: R -> R be a differentiable function with g(0) = 0,,g'(1)!=0 .Let f(x)={x/|x|g(x), 0 !=0 and 0,x=0 and h(x)=e^(|x|) for all x in R . Let (foh)(x) denote f(h(x)) and (hof)(x) denote h(f(x)) . Then which of the following is (are) true? A. f is differentiable at x = 0 B. h is differentiable at x = 0 C. f o h is differentiable at x = 0 D. h o f is differentiable at x = 0

If f:R→R, g:R→R be two given functions, then f(x)=2min{∣f(x)−g(x)∣,0} equals

Let f : R rarr R be the signum function defined as f(x)= {{:(1,x gt0),(0,x=0),(-1,x lt0):} and g :R rarr be the greatest integer function given by g(x) = [x] . Then prove that fog and gof coincide in [-1,0).

Let f: R->R be the Signum Function defined as f(x)={1,x >0; 0,x=0; -1,x R be the Greatest Integer Function given by g(x) = [x] , where [x] is greatest integer less than or equal to x. Then does fog and gof coincide in (0,1]

Let f:R rarr R and g:R rarr R be two functions such that fog(x)=sin x^(2) andgo f(x)=sin^(2)x Then,find f(x) and g(x)

Let f and g be two functions from R into R defined by f(x) =|x|+x and g(x) = x " for all " x in R . Find f o g and g o f

Let a real valued function f satisfy f(x + y) = f(x)f(y)AA x, y in R and f(0)!=0 Then g(x)=f(x)/(1+[f(x)]^2) is