Home
Class 12
MATHS
If f(x) = -1 +|x-1|, -1 le x le 3 " and ...

If `f(x) = -1 +|x-1|, -1 le x le 3 " and " g(x)=2-|x+1|, -2 le x le 2,` then find `fog(x) " and " gof(x).`

Text Solution

AI Generated Solution

To find \( f(g(x)) \) and \( g(f(x)) \) for the given functions \( f(x) = -1 + |x - 1| \) for \( -1 \leq x \leq 3 \) and \( g(x) = 2 - |x + 1| \) for \( -2 \leq x \leq 2 \), we will follow these steps: ### Step 1: Find \( g(x) \) First, we need to evaluate \( g(x) \): \[ g(x) = 2 - |x + 1| ...
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Solved Examples|15 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.1|15 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE ENGLISH|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Two functions are defined as under : f(x)={(x+1, x le 1), (2x+1, 1 < x le 2):} and g(x)={(x^2, -1 le x le 2), (x+2, 2 le x le 3):} Find fog and gof

If f(x) = {{:( 3x ^(2) + 12 x - 1",", - 1 le x le 2), (37- x",", 2 lt x le 3):}, then

Let f(x) and g(x) be two functions given by f(x)=-1|x-1|,-1 le x le 3 and g(x)=2-|x+1|,-2 le x le 2 Then,

Solve 1 le |x-2| le 3

If f (x)= {{:(1+x, 0 le x le 2),( 3x-2, 2 lt x le 3):}, then f (f(x)) is not differentiable at:

if f(x) = {[3x+4 , 0 le x le 2],[5x , 2 le x le 3]}, then evaluate int_(0)^(3) f(x) dx.

If the function f(x) ={x+1 if x le 1 , 2x+1 if 1 lt x le 2 and g(x) = {x^2 if -1 le x le 2 , x+2 if 2 le x le 3 then the number of roots of the equation f(g(x))=2

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

Suppose f:[-2,2] to R is defined by f(x)={{:(-1 " for " -2 le x le 0),(x-1 " for " 0 le x le 2):} , then {x in [-2,2]: x le 0 and f(|x|)=x}=

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