f is a continous function in `[a, b]`; g is a continuous function in [b,c]. A function h(x) is defined as `h(x)=f(x) for x in [a,b) , g(x) for x in (b,c]` if f(b) =g(b) then

Is the function defined by f(x)= |x| , a continuous function?

If f and g are continuous functions with f(3)=5 and lim_(x to 3)[2f(x)-g(x)]=4 , find g(3).

If f and g are continuous functions with f(3) = 5 and lim_(xto3)[2f(x)-g(x)]=4 , find g(3).

If f(x)a n dg(x) are continuous functions in [a , b] and are differentiable in (a , b) then prove that there exists at least one c in (a , b) for which. |f(a)f(b)g(a)g(b)|=(b-a)|f(a)f^(prime)(c)g(a)g^(prime)(c)|,w h e r ea

Let f be a function defined on [0,2]. Then find the domain of function g(x)=f(9x^2-1)

if the function f(x)=AX-B X =2 is continuous at x=1 and discontinuous at x=2 find the value of A and B

Which of the following statements is always true? ([.] represents the greatest integer function. a) If f(x) is discontinuous then |f(x)| is discontinuous b) If f(x) is discontinuous then f(|x|) is discontinuous c) f(x)=[g(x)] is discontinous when g(x) is an integer d) none of these

Let f(x) and phi(x) are two continuous function on R satisfying phi(x)=int_(a)^(x)f(t)dt, a!=0 and another continuous function g(x) satisfying g(x+alpha)+g(x)=0AA x epsilonR, alpha gt0 , and int_(b)^(2k)g(t)dt is independent of b If f(x) is an even function, then

Which of the following functions has inverse function? a) f: ZrarrZ defined by f(x)=x+2 b) f: ZrarrZ defined by f(x)=2x c) f: ZrarrZ defined byy f(x)=x d) f: ZrarrZ defined by f(x)=|x|