Let f(x)={{:(,|x|-3,x lt 1),(,|x-2|+a,x ...

Let `f(x)={{:(,|x|-3,x lt 1),(,|x-2|+a,x ge 1):}`
`g(x)={{:(,2-|x|,x lt 1),(,Sgn(x)-b,x ge 1):}` If h(x)=f(x) is discontinuous at exactly one point, then which of the following are correct?

A

`a=-3, b=0`

B

`a=-3,b=-1`

C

`a=2,b=1`

D

`a=0,b=1`

Text Solution

Verified by Experts

The correct Answer is:

A, B, C, D

Promotional Banner

Promotional Banner

Topper's Solved these Questions

CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|32 Videos
CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (MATHCING TYPE PROBLEMS)|1 Videos
CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|23 Videos
COMPOUND ANGLES
VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-5 : Subjective Type Problems|31 Videos
DETERMINANTS
VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|12 Videos

Similar Questions

Explore conceptually related problems

Let f(x)={{:(,|x|-3,x lt 1),(,|x-2|+a,x ge 1):} g(x)={{:(,2-|x|,x lt 1),(,Sgn(x)-b,x ge 1):} If h(x)=f(x)+g(x) is discontinuous at exactly one point, then which of the following are correct?

If f(x)={|x|-3 x = 1 & g(x)={2-|x| x = 2. if h(x)=f(x)+g(x) is discontinuous at exactly one point, then -

Let f(x)={{:(x+a,","x lt 0),(|x-1|,","x ge 0):} and g(x)={{:(x+1,", if " x lt 0),((x-1)^2+b ,"," x ge 0):} If gof is continuous (a gt 0) then

Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}

Let f(x)={{:(x^(3)-1",", x lt2),(x^(2)+3"," , x ge 2):} Then

f(x)={(log_(e)x",",0lt x lt 1),(x^(2)-1 ",",x ge 1):} and g(x)={(x+1",",x lt 2),(x^(2)-1 ",",x ge 2):} . Then find g(f(x)).

show that f(x) ={{:( (2x-1)",",if , x lt2),( (3x)/2",,if x ge 2):} is continuous

VIKAS GUPTA (BLACK BOOK)-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)

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 f:RtoR is given by f(x)={(p+qx+x^(2),xlt2),(2px+3qx^(2),xge2):} t...
Text Solution
|
If y =e ^(x sin (x ^(3)))+(tan x)^(x) then (dy)/(dx) may be equal to:
Text Solution
|
Let f(x)=x+(1-x)x^3+(1-x)(1-x^2)x^3+.........+(1-x)(1-x^2)........(1-x...
Text Solution
|
Let f (x)= [{:(x ^(2)+a,0 le x lt 1),( 2x+b,1le x le 2):}and g (x)=[{:...
Text Solution
|
If f (x)= [{:((sin [x^(2)]pi)/(x ^(2)-3x+8)+ax ^(3)+b,,, 0 le x le 1),...
Text Solution
|
If f (x)= {{:(1+x, 0 le x le 2),( 3x-2, 2 lt x le 3):}, then f (f(x)) ...
Text Solution
|
Let f (x)=(x+1) (x+2) (x+3)…..(x+100) and g (x) =f (x) f''(x) -f ('(x)...
Text Solution
|
Let f(x)={{:(,|x|-3,x lt 1),(,|x-2|+a,x ge 1):} g(x)={{:(,2-|x|,x lt...
Text Solution
|
Let f (x) be a continous function in [-1,1] such that f (x)= [{:((ln...
Text Solution
|
f (x) is differentiable function satisfying the relationship f ^(2) (x...
Text Solution
|
The function f (x)=[sqrt(1-sqrt(1-x ^(2)))],(where [.] denotes greates...
Text Solution
|
A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y),...
Text Solution
|
The points of discontinuities of f (x)= [(6x)/(pi)]cos [(3x)/(pi)]"in"...
Text Solution
|
If f(x)={{:(,(x^(2))/(2),0 le x lt 1),(,2x^(2)-3x+(3)/(2),1 le x le 2)...
Text Solution
|
If x=phi(t),y=Psi(t)," then "(d^(2)y)/(dx^(2)) is equal to
Text Solution
|
f (x)=[x] and g (x)= {{:( 0"," , x in I ),( x ^(2)"," , cancel(in)I)...
Text Solution
|
Let f : R ^(+) to R defined as f (x)= e ^(x) + ln x and g = f ^(-1) th...
Text Solution
|
Let f (x)=[{:((3x-x ^(2))/(2),,, x lt 2),([x-1],,, 2 le x lt 3),( x ^(...
Text Solution
|