Home
Class 12
MATHS
Let f(x)={{:(x^(2)-4x+3",", x lt 3),(x-4...

Let `f(x)={{:(x^(2)-4x+3",", x lt 3),(x-4",", x ge 3):}`
and `g(x)={{:(x-3",", x lt 4),(x^(2)+2x+2",", x ge4):}`, which one of the following is/are true?(f+g)(3.5)=0 f(g(3))=3,f(g(2))=1,(f-g)(4)=0

A

(f+g)(3.5)=0

B

f(gh(3))=3

C

f(g(2))=1

D

(f-g)(4)=0

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Similar Questions

Explore conceptually related problems

If f(x) = {{:(x - 3",",x lt 0),(x^(2) - 3x + 2",",x ge 0):} , then g(x) = f(|x|) is

Let f and g be real valued functions defined as f(x)={{:(7x^(2)+x-8",",xle 1),(4x+5",",1lt x le 7),(8x+3",",x gt7):} " " g(x)={{:(|x|",",xlt -3),(0",",-3le x lt 2),(x^(2)+4",",xge 2):} The value of (gof) (0) + (fog) (-3) is

Let f and g be real valued functions defined as f(x)={{:(7x^(2)+x-8",",xle 1),(4x+5",",1lt x le 7),(8x+3",",x gt7):} " " g(x)={{:(|x|",",xlt -3),(0",",-3le x lt 2),(x^(2)+4",",xge 2):} The value of 4(gof) (2) - (fog) (9) is

Let f and g be real valued functions defined as f(x)={{:(7x^(2)+x-8",",xle 1),(4x+5",",1lt x le 7),(8x+3",",x gt7):} " " g(x)={{:(|x|",",xlt -3),(0",",-3le x lt 2),(x^(2)+4",",xge 2):} The value of 2(fog) (7) - (gof) (6) is

f(x)= {(|x|+3",","if" x le -3),(-2x",","if"-3 lt x lt 3),(6x + 2 ",","if " x ge 3):}

f(x)= {(|x+1|",",x lt -2),(2x+3",",-2 le x lt 0),(x^(2) + 3",",0 le x lt 3),(x^(3)-15,3 le x):} . Find at which points, the function f(x) is discontinuous ?

f(x)= {((1)/(2)-x ",",0 le x lt (1)/(2)),(1",",x= (1)/(2)),((3)/(2)-x",",(1)/(2) lt x le 1):} Discuss the continuity of f(x)

f(x) = {(3",","if" 0 le x le 1),(4",","if" 1 lt x lt 3),(5",","if" 3 le x le 10):}

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