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

Options

A. 4
B. 3
C. 2
D. 1

Answer

C

Explanation

`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