If `f(x)={x-4 , if x leq 5 and 5x- 24 , if x<5` prove that `f(x)` is continuous at `x= 5`.

If (x)={x-4,quad if x<=5 and 5x-24,quad if x

If f(x) = {sinx , x lt 0 and cosx-|x-1| , x leq 0 then g(x) = f(|x|) is non-differentiable for

Let f_1(x)={x, x leq x leq 1 and 1 x gt1 and 0 ,otherwise f_2(x) =f_1 (-x) for all x abd f_3(x)=-f_2(x) for all x and f_4(x)=-f_3(-x) for all x Which of the following is necessarily true?

Let f_1(x)={x, x leq x leq 1 and 1 x gt1 and 0 ,otherwise f_2(x) =f_1 (-x) for all x abd f_3(x)=-f_2(x) for all x and f_4(x)=-f_3(-x) for all x Which of the following is necessarily true?

Let f(x)=1+x , 0 leq x leq 2 and f(x)=3−x , 2 lt x leq 3 . Find f(f(x)) .

Show that the function f(x)={(x-4", "x le 5),(5x-24", "xgt5):} is cotinuous at x=5.

Show that the function f(x)={(x-4", "x le 5),(5x-24", "xgt5):} is cotinuous at x=5.

If f(x)=sgn(x-2) xx [In x], 1leq x leq 3 and {x^2} ,-3 lt x leq 3.5 where [.] denotes the greatest integer function and {.} represents the fractional part functon, then the number of points of discontinuity in [1,3.5] is

If f(x) = |(x - 4) (x - 5)| , then f'(x) is