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Let f(x) :R->R,f(x)={(2x+alpha^2,xge2),(...

Let `f(x) :R->R,f(x)={(2x+alpha^2,xge2),((alpha x)/2+10,x lt 2))` If `f(x)` is onto function then `alpha` belongs to (A) `[1,4]` (B) `[-2,3]` (C) `[0,3]` (D) `[2,5]`

A

`[1,4]`

B

`[-2,3]`

C

`(0,3]`

D

`[2,5}`

Text Solution

Verified by Experts

The correct Answer is:
C

Clearly from graph
we must have
`2(2)+alpha^() le alpha+10`
`therefore" "(alpha-3)(alpha+2)le0`
`therefore" "alpha in [-2,3]`
Also `alpha gt 0`
`therefore" "alpha in (0,3]`
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