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Let f(x) be a function whose domain is [...

Let f(x) be a function whose domain is `[-5, 7] and g(x) = |2x + 5|,` then the domain of fog(x) is (A) `[-5,1]` (B) `[-4,0]` (C) `[-6,1]` (D) none of these

A

`[-4,1]`

B

`[-5,1]`

C

`[-6,1]`

D

`[-3,1]`

Text Solution

Verified by Experts

The correct Answer is:
C
Domain of `f(g(x))`
Range of `g(x)-=` Domain of `f(x)`
`implies-5le|2x+5|le7`
`implies0le|2x+5|le7`
`implies-7le2x+5le7`
`implies-12le2xle2`
`implies-6lexle1`
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