Q. Let `f:[a,b]->[1,oo)` be a continuous function and let `g:R->R` be defined as g(x)={0 if x< a , `int_a^x f(t)dt` if `a<=x<=b ` , `int_a^b f(t)dt if x >b `

Let f:[a , b]vec[1,oo) be a continuous function and let g: RvecR be defined as g(x)={0ifx bT h e n g(x) is continuous but not differentiable at a g(x) is differentiable on R g(x) is continuous but nut differentiable at b g(x) is continuous and differentiable at either a or b but not both.

Let, f:[a,b]to[1,oo) be a continuous function and let g:RR to RR be defined as g(x)={{:(0,"if "x lta","),(int_(a)^(x)f(t)dt,"if "alexleb),(int_(a)^(b)f(t)dt,"if "x gtb):} Then

Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined as g(x)={(0,"if",xlta),(int_(a)^(x)f(t)dt,"if",alexleb),(int_(a)^(b)f(t)dt,"if",xgtb):} Then

Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined as g(x)={(0,"if",xlta),(int_(a)^(x)f(t)dt,"if",alexleb),(int_(a)^(b)f(t)dt,"if",xgtb):} Then

Let f be continuous and the function g is defined as g(x)=int_0^x(t^2int_0^tf(u)du)dt where f(1) = 3 . then the value of g' (1) +g''(1) is

Let f: R->R be any function. Also g: R->R is defined by g(x)=|f(x)| for all xdot Then g is a. Onto if f is onto b. One-one if f is one-one c. Continuous if f is continuous d. None of these

Let f: R->R be any function. Also g: R->R is defined by g(x)=|f(x)| for all xdot Then g is a. Onto if f is onto b. One-one if f is one-one c. Continuous if f is continuous d. None of these

Let [x] denote the integral part of x in R and g(x) = x- [x] . Let f(x) be any continuous function with f(0) = f(1) then the function h(x) = f(g(x) :

Let [x] denote the integral part of x in R and g(x) = x- [x] . Let f(x) be any continuous function with f(0) = f(1) then the function h(x) = f(g(x) :