Question

Find the domain and the range of each of the functions given below.
(i) `f(x)=|x-1|` (ii) `g(x)=-|x|`

Answer 1

(i) We have, `f(x)=|x-1|`
Clearly, f(x) is defined for all `x""inR`. So, dom (f)=R. For all `x""inR`, we have
`|x-1|ge0impliesf(x)ge0`.
`:." range "(f)=[0,oo)`.
Hence, dom (f)=R and range `(f)=[0,oo)`.
(ii) We have, `g(x)=-|x|`.
Clearly, g(x) is defined for all `x""inR`. So, dom (g)=R. For all `x""inR` we have
`|x|ge0implies-|x|le0impliesg(x)le0`.
`:."range "(g)=(-oo,0]`.
Hence, dom (g)=R and range (g) `=(-oo,0]`.