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Let f(x)={(2x+a",",x ge -1),(bx^(2)+3","...

Let `f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):}`
and `g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):}`
If the domain of `g(f(x))" is " [-1, 4],` then

A

`a=1, b gt 5`

B

`a=2, b gt 7`

C

`a=2, b gt 10`

D

`a=0, b in R`

Text Solution

Verified by Experts

The correct Answer is:
D
`x in [-1,2]`
`or -1 le x le 2`
`or -2 le 2x le 4`
`or -2+a le 2x+a le 4+a`
`or -2+a le -2 and 4+a le 4, i.e., a=0`
b can take any value.
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