Home
Class 12
MATHS
f(x)={(x-1",",-1 le x le 0),(x^(2)",",0l...

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

A

It is a periodic function with period `pi`

B

The range is [0, 1]

C

Domain R

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Matching Type Questions|1 Videos
  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|3 Videos
  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|2 Videos
  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|24 Videos
  • HYPERBOLA

    ARIHANT MATHS|Exercise Hyperbola Exercise 11 : Questions Asked in Previous 13 Years Exams|3 Videos

Similar Questions

Explore conceptually related problems

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

Let f (x) { {:(1+x"," , 0 le x le 2),( 3-x"," ,2 lt x le 3):}: Find fof.

If the functions f(x)=x^(3)+e^(x//2) " and " g(x)=f^(-1)(x) , the value of g'(1) is ………… .

Consider the function f(x) = {{:(x{x}+1",","if",0 le x lt 1),(2-{x}",","if",1 le x le 2):} , where {x} denotes the fractional part function. Which one of the following statements is not correct ?

Let f(x)={(x+1",", x lt1),(2x+1",",1lt x le 2):}" and " g(x)={(x^(3)",", -1 le x lt 2),(x+2",",2 le x le 3):} find fog(x) .

If f(x) = {{:(|1-4x^(2)|",",0 le x lt 1),([x^(2)-2x]",",1 le x lt 2):} , where [] denotes the greatest integer function, then

f(x)=abs(x-1)+abs(x-2), -1 le x le 3 . Find the range of f(x).

{:(f(x) = cos x and H_(1)(x) = min{f(t), 0 le t lt x},),(0 le x le (pi)/(2) = (pi)/(2)-x,(pi)/(2) lt x le pi),(f(x) = cos x and H_(2) (x) = max {f(t), o le t le x},),(0 le x le (pi)/(2) = (pi)/(2) - x","(pi)/(2) lt x le pi),(g(x) = sin x and H_(3)(x) = min{g(t),0 le t le x},),(0 le x le (pi)/(2)=(pi)/(2) - x, (pi)/(2) le x le pi),(g(x) = sin x and H_(4)(x) = max{g(t),0 le t le x},),(0 le x le (pi)/(2) = (pi)/(2) - x, (pi)/(2) lt x le pi):} Which of the following is true for H_(1) (x) ?

Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x le 0),(x-1",",1 lt x le 2):} and g(x)=f(|x|) +|f(x)| . Then find g(x) .

If f(x)=sinx,g(x)=x^(2)andh(x)=logx. IF F(x)=h(f(g(x))), then F'(x) is