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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 `a=2 and b=3,` then the range of `g(f(x))` is

A

`(-2,8]`

B

`(0, 8]`

C

`[4, 8]`

D

`[-1, 8]`

Text Solution

Verified by Experts

The correct Answer is:
C
If `a=2, b=3,`
`f(x)={(2x+2",",x ge -1),(3x^(2)+3",",x lt -1):}`
The range of `f(x)` is `[0,oo).`
` :. g(f(x))=2x+6,-1 le x le 1`
So, range of `g(f(x)) " is " [4,8].`
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