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If f(x)=sqrt(x)" and "g(x)=2x-3, then do...

If `f(x)=sqrt(x)" and "g(x)=2x-3`, then domain of (fog) (x) is

A

`(-oo,-3)`

B

`(-oo,-(3)/(2))`

C

`[-(3)/(2),0]`

D

`[(3)/(2),oo]`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `f(x)=sqrt(x)" and "g(x)=2x-3`
`:."fog"(x)=f{g(x)}=f(2x-3)=sqrt(2x-3)`
For domain of fog(x),
`2x-3ge0implies2xge3impliesxge(3)/(2)`
`:." "x in[(3)/(2),oo]`
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