A function defined by `f(x)=x+a` for `x lt 0; x` for `0 leq x lt 1; b-x` for `x geq 1` is continuous in `[-2,2].` Show that `(a+b)` is even

A functon f(x) is defined as f(x)=x+a, "for" x lt0 =x, "for" 0lex lt1, =b-x, "for" x ge 1 is continous on its domain. Find a+b.

If function defined by f(x) ={(x-m)/(|x-m|) , x leq 0 and 2x^2+3ax+b , 0 lt x lt 1 and m^2x+b-2 , x leq 1 , is continuous and differentiable everywhere ,

If f(x) is continuous in [-2, 2], where f(x)={:{(x+a", for " x lt 0),(x", for " 0 le x lt 1),(b-x", for " x ge 1):} , then a+b=

The function f(x) is defined by f(x)={x^2+a x+b\ \ \ ,\ \ \ 0lt=x 4 f is continuous them determine the value of a and b

The function f(x) is defined by f(x)={x^2+a x+b\ \ \ ,\ \ \ 0lt=x 4 f is continuous them determine the value of a and b

Given a function defined by y = f(x) = sqrt(4- x^(2)) 0 lt= x lt= 2 , 0 lt= y lt=2. Show that f is bijective function .

Let f(x)={{:(ax-b,","x le 1),(3x,"," 1 lt x lt 2),(bx^2-a,"," x ge 2):} If f is continuous function then (a,b) is equal to

At x =1, the function given by f(x) = {(sinx,x lt 0),(2x,x ge 0):} is (a) Continuous (b) Not continuous ( c) Not defined

A function f(x) is defined in a lt x lt b and a lt x_(1) lt x_(2) lt b , then f(x) is strictly monotonic decreasing in a le x le b when-