Let `f(x)` be a function whose domain is `[-5,7]`. Let `g(x)=|2x+5|`, then domain of `(fog)(x)` is

Options

A. `[-5, 1 ]`
B. ` [-4, 0]`
C. ` [ -6, 1]`
D. none of these

Answer

C

Explanation

We have,
`"Domain" (fog)={x :x in Dom (g) and g(x) in Dom (f)}`
`rArr "Domain" (fog) = {x:x in R and |2x +5| in [-5,7]}`
`rArr "Domain" (fog) ={ x : - 5 le|2x + 5| le 7}`
`rArr " Domain" (fog) ={ x : 0 le|2x + 5| le 7}`
`rArr "Domain" (fog) = {x: | 2x + 5| le 7}`
`rArr "Domain" (fog) = {x: -7 le 2x + 5 le7}`
`rArr "Domain" (fog) = { x: - 12 le 2x le2}`
`rArr "Domain" (fog) ={ x: - 6 le x le 1} = [-6,1]`