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If the function f(x) ={x+1 if x le 1 , ...

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`

A

4

B

3

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
`f(g(x))={{:(x^(2)+1,-1lexle1),(2x^(2)+1,1ltxlesqrt2):}`
`f(g(x))=2 rArr x^(2)+1=2 and 2x^(2)+1=2`
`rArr" "x=pm 1, x=pm(1)/(sqrt2)`
No. of solutions = 2
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