Let `f(x)=(x+|x|)|x|` . Then, for all `x` `f` is continuous

Let f(x)=|x|+|x-1|, then (a) f(x) is continuous at x=0, as well at x=1 (b) f(x) is continuous at x=0, but not at x=1 (c) f(x) is continuous at x=1, but not at x=0 (d)none of these

Let f be a function such that f(x+y)=f(x)+f(y) for all xa n dya n df(x)=(2x^2+3x)g(x) for all x , where g(x) is continuous and g(0)=3. Then find f^(prime)(x)dot

Let f be a function such that f(x+y)=f(x)+f(y) for all xa n dya n df(x)=(2x^2+3x)g(x) for all x , where g(x) is continuous and g(0)=3. Then find f^(prime)(x)dot

Let f(x)={1, x =1 . Then, f is (a) continuous at x=-1 (b) differentiable at x=-1 (c) everywhere continuous (d) everywhere differentiable

Statement-1: If |f(x)| le |x| for all x in R then |f(x)| is continuous at 0. Statement-2: If f(x) is continuous then |f(x)| is also continuous.

Let f(x) = sin"" 1/x, x ne 0 Then f(x) can be continuous at x =0

Let f(x) be defined for all x > 0 and be continuous. Let f(x) satisfies f(x/y)=f(x)-f(y) for all x,y and f(e)=1. Then (a) f(x) is unbounded (b) f(1/x)vec 0 as x vec0 (c) f(x) is bounded (d) f(x)=(log)_e x

If f(x)=|(log)_e|x|| , then (a) f(x) is continuous and differentiable for all x in its domain] (b) f(x) is continuous for all x in its domain but not differentiable at x=+-1 (c) f(x) is neither continuous nor differentiable at x=+-1 (d) none of these

A function f(x) satisfies the following property: f(xdoty)=f(x)f(y)dot Show that the function f(x) is continuous for all values of x if it is continuous at x=1.

Let f(x)=x^3-6x^2+15 x+3 . Then, (a) f(x)>0 for all x in R (b) f(x)>f(x+1) for all x in R (c) f(x) is invertible (d) f(x)<0 for all x in R