Let g(x)=1+x-[x] and f(x)={-1,x < 0 0,...

Let `g(x)=1+x-[x] and f(x)={-1,x < 0 0, x=0 1, x > 0.` Then for all `x,f(g(x))` is equal to (where [.] represents the greatest integer function). (a) `x` (b) `1` (c) `f(x)` (d) `g(x)`

A

x

B

1

C

f(x)

D

g(x)

Text Solution

Verified by Experts

The correct Answer is:

B

We have ,
`g(x)=1+x-[x] ge1 ` for all ` x in R `
`:. f(g(x)) =1 ` for all ` x in R `

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