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If f(x)={(|x|-3 when x < 1), and (|x-2|...

If `f(x)={(|x|-3` when ` x < 1)`, and `(|x-2|+a ,` when `x >= 1)` &
`g(x)={2-|x| `when ` x < 2` and `sgn(x)-b` , when `x >= 2`.
if `h(x)=f(x)+g(x)` is discontinuous at exactly one point, then -
(a). `a=-3, b=0`
(b). `a=-3, b=-1 `
(c) `a=2, b=1`
(d) `a=0, b=1`

A

`a=-3,b=0`

B

`a=0,b=1`

C

`a=2,b=1`

D

`a=-3,b=1`

Text Solution

Verified by Experts

The correct Answer is:
D
`h(x)=f(x)+g(x)`
`={{:(-1",",-ooltxlt1),(a+4-2x",",1lexlt2),(a-b-1+x",",2lexltoo):}`
`therefore" We must have either "a=-3, b ne 1 or b=1, a ne -3`
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