If `f(x)={{:(-e^(-x)+k,",",xle0),(e^(x)+1,",",0ltxlt1),(ex^(2)+lambda,",",xge1):}` is one-one and monotonically increasing `AA x in R`, then

f(x)=x+(1)/(x),x!=0 is monotonic increasing when

If f(x)={(sinx-e^x, ,x lt 0),(a+[-x],,0lexlt1),(2x-b,,xge1):} is continuous in (-oo,1] , find the value of a+b

If f(x)={{:(x^(3)(1-x)",",xle0),(xlog_(e)x+3x",",xgt0):} then which of the following is not true?

If f(x)={{:(x^(3)(1-x)",",xle0),(xlog_(e)x+3x",",xgt0):} then which of the following is not true?

If f(x)={{:(x^(3)(1-x)",",xle0),(xlog_(e)x+3x",",xgt0):} then which of the following is not true?

Let a function f : R to R be defined as f(x)={{:(sinx-e^(x),if,xle0),(a+[-x],if,0ltxlt1),(2x-b,if,xge1):} Where [x] is the greatest integer less than or equal to x. If f is continuous on R, then (a + b) is equal to:

Let f(x) =e^(2x) -ae^(x)+1. Prove that f(x) cannot be monotonically decreasing for AA x in R for any value of a

If a lt 0, f(x) = e^(ax) + e^(-ax) and S = {x: f(x) is monotonically increasing} then S equals,