f (x)= {{:(2(x+1),,, x le -1),( sqrt(1- ...

`f (x)= {{:(2(x+1),,, x le -1),( sqrt(1- x^(2)),,, -1 lt x lt 1), (|||x|-1|-1|,,, x ge1 ):}`, then:

f (x) is non-differentialbe at exactly three points

f (x) is continous in `(-oo,1]`

`f(x)` is differentiable in `(-oo, -1]`

f (x) is finite type of discontinuity at `x=1,` but continous at `x=-1`

Text Solution

Verified by Experts

The correct Answer is:

A, C, D

Topper's Solved these Questions

CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VK JAISWAL|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|32 Videos
CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VK JAISWAL|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|1 Videos
CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VK JAISWAL|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|23 Videos
COMPOUND ANGLES
VK JAISWAL|Exercise Exercise-5 : Subjective Type Problems|31 Videos
DETERMINANTS
VK JAISWAL|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|11 Videos

Similar Questions

Explore conceptually related problems

The value(s) of x for which the function f(x) = {(1-x, ",", x lt 1),((1-x)(2-x), ",", 1 le x le 2 ),(3-x, ",", x gt 2 ):} fails to be continuous is (are)

f(x) {{:(x + 1"," if x ge 1 ),(x^(2)+ 1"," if x lt 1):}

The function f(x) = min {|x|, sqrt(1-x^(2))}, -1lt x lt 1 possesses

Consider a function defined in [-2,2] f (x)={{:({x}, -2 lle x lt -1),( |sgn x|, -1 le x le 1),( {-x}, 1 lt x le 2):}, where {.} denotes the fractional part function. The total number of points of discontinuity of f (x) for x in[-2,2] is:

If f(x)={:{(-2", for " x le -1),(2x", for " -1 lt x le 1),(2", for " x gt 1):} , then

f(x) {{:(-2"," if x le -1),(2x"," if -1lt x le 1),(2"," if x gt 1):}

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

If f(x) is continuous in [-2,2], where f(x) = {((sinax)/(x)-2,",","for" -2 le x lt 0),(2x+1,",","for"0 le x le 1),(2bsqrt(x^(2)+3)-1,",","for" 1 lt x le 2):} , then the value of (a+b) is

VK JAISWAL-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)

If f (x)= tan ^(-1) (sgn (x ^(2) -lamda x+1)) has exactly one point of...
Text Solution
|
f (x)= {{:(2(x+1),,, x le -1),( sqrt(1- x^(2)),,, -1 lt x lt 1), (|||x...
Text Solution
|
Let f (x)= [{:((x(3e^(1//x)+4))/(2 -e^(1//x)),,,( x ne 0)),(0 ,,, x=0)...
Text Solution
|
Let |f (x)| le sin ^(2) x, AA x in R, then
Text Solution
|
Let f (x)=[{:((a (1-x sin x)+ b cos x +5)/(x ^(2)),,, x lt 0), ((1+ ((...
Text Solution
|
If f (x)=|||x|-2|+p| have more than 3 points non-derivability then the...
Text Solution
|
Identify the options having correct statement:
Text Solution
|
A twice differentiable function f(x)is defined for all real numbers an...
Text Solution
|
If f(x) = |sinx|, then
Text Solution
|
Let [.] represent the greatest integer function and f (x)=[tan^2 x] th...
Text Solution
|
Let f be a differentiable function satisfying f'(x)=f' (-x) AA x in R....
Text Solution
|
Let f :R to R be a function, such that |f(x)|le x ^(4n), n in N AA n i...
Text Solution
|
Let f (x) =[x] and g (x) =0 when x is an integer and g (x) =x ^(2) whe...
Text Solution
|
Let f:RtoR is given by f(x)={(p+qx+x^(2),xlt2),(2px+3qx^(2),xge2):} t...
Text Solution
|
Let f (x) =|2x-9|+|2x+9|. Which of the following are true ?
Text Solution
|
Let f (x)= max (x,x ^(2) x ^(3)) in -2 le x le 2. Then:
Text Solution
|
Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA, x...
Text Solution
|
Let f(x) =(x^(2)-3x+ 2) (x ^(2) + 3x +2) and alpha, beta, gamma satisf...
Text Solution
|
let the function f be defined by f (x)= {{:(p+ qx+ x^(2)"," , x lt 2),...
Text Solution
|
If y =e ^(x sin (x ^(3)))+(tan x)^(x) then (dy)/(dx) may be equal to:
Text Solution
|