Consider the function f(x)=f(x)={{:(x-1"...

Consider the function `f(x)=f(x)={{:(x-1",",-1lexle0),(x^(2)",", 0lexle1):}`
and`" "g(x)=sinx.`
If `h_(1)(x)=f(|g(x)|)`
`" and "h_(2)(x)=|f(g(x))|.`
Which of the following is not true about `h_(2)(x)`?

A

h(x) is continuous for `x in [-1, 1]`

B

h(x) is differentiable for `x in [-1, 1]`

C

h(x) is differentiable for `x in [-1, 1] - {0}`

D

h(x) is differentiable for `x in (-1, `)-{0}`

Verified by Experts

The correct Answer is:

C

Similar Questions

Explore conceptually related problems

f(x)={{:(x-1",", -1 le x 0),(x^(2)",",0 lt x le 1):} and g(x)=sinx. Find h(x)=f(abs(g(x)))+abs(f(g(x))).

If f(x) = {{:(x - 3",",x lt 0),(x^(2) - 3x + 2",",x ge 0):} , then g(x) = f(|x|) is

f(x)= x, g(x)= (1)/(x) and h(x)= f(x) g(x). If h(x) = 1 then…….

If f(x)= 2x and g(x) = (x^(2))/(2) + 1 , then which of the following can be a discontinuous function?

Is the function f defined by f(x)= {(x",","if" x le 1),(5",","if" x gt 1):} continuous at x=0 ? At x= 1 ? At x=2 ?

Let g(x)=1+x-[x] "and " f(x)={{:(-1","x lt 0),(0","x=0),(1","x gt 0):} Then, for all x, find f(g(x)).

f(x)= (1)/((x-1) (x-2)) and g(x)= (1)/(x^(2)) . Find the points of discontinuity of the composite function f(g(x))?

If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x) , then the value of g'(1) is

If the functions f(x)=x^(5)+e^(x//3) " and " g(x)=f^(-1)(x) , the value of g'(1) is ………… .