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

`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))).`

Text Solution

Verified by Experts

The correct Answer is:
h(x)=`{{:(2sinx",", -1 lt x lt 0),(2sin^(2)x",", 0 lt x le 1):}`
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 11|2 Videos
  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 12|4 Videos
  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 9|10 Videos
  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos
  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

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) ?

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) .

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

If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt x le 2,, and g(x) = int_(0)^(x) f(t ) dt","),( x- e,,"," 2lt x le 3 ,, ""):} x in [ 1, 3 ] , then a. g(x) has local maxima at x=1+log_(e)2 and local minima at x=e b. f(x) has local maxima at x=1 and local minima at x=2 c. g(x) has no local minima d. f(x) has no local maxima

If f(x) = {{:(x - 3",",x lt 0),(x^(2) - 3x + 2",",x ge 0):} , then g(x) = f(|x|) is a. g'(0^(+)) = - 3 b. g'(0^(-)) = -3 c. g'(0^(+)) = g'(0^(-)) d. g(x) is not continuous at x = 0

Evaluate the left-hand and right-hand limits of the a following function at x =1 : f(x)={{:(5x-4",", "if "0 lt x le 1), (4x^(2)-3x",", "if "1 lt x lt 2.):} Does lim_(x to 1)f(x) exist ?

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then a. f(x) is differentiable at x = 0 and x = 1 b. f(x) is differentiable at x = 0 but not at x = 1 c. f(x) is not differentiable at x = 1 but not at x = 0 d. f(x) is not differentiable at x = 0 and x = 1

Show that the function f(x) = {{:(2x+3",",-3 le x lt -2),(x+1",",-2 le x lt 0),(x+2",",0 le x le 1):} is discontinuous at x = 0 and continuous at every point in interval [-3, 1]