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

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:

If f(x)={{:((sin(a+1)x+2sinx)/x", "xlt0),(2" ,"x=0),((sqrt(1+bx)-1)/x" ,"xgt0):} is continuous at x = 0, then find the values of 'a' and 'b'.

If the function f(x) = {(1+(sin)(pi x)/2,",","for"-oo lt x le 1),(ax+b, ",","for" 1 lt x lt 3),(6(tan)(pi x)/12,",","for"3 le x lt 6):} is continuous in the interval (-oo, 6) , then the value of a and b are respectively

Find 'a' and 'b' if the function : f(x)={{:((sinx)/(x)" , "-2lexlt0),(a.2^(x)" , "0lexle1),(b+x", "1ltxle2):} is a continuous function on [-2, 2].

Let f(x)= {:{((x+a) , x lt1),( ax^(2)+1, xge1):} then f(x) is continuous at x =1 for

Let f is defined by the following function f(x) = {(sinx, x lt 0), (x^2, 0lex lt 1),(2-x,1 le x le 2),(x-3,xge 2):} For what value of x, f is not continuous ?

Let f(x)={{:(3x^(2)-4sqrtx+1,"for",xlt1),(ax+b,"for",xge1):} If f(x) is continuous and differentiable for all real values in its domain then

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