Find the rage of each of the following functions. (i) `f(x)" "=" "2" "" "3x ," "x in R , x" ">" "0` (ii) `f(x)" "=x^2+" "2` , x is a real number. (iii) `f(x)" "=" "x` , x is a real number.

Answer

N/a

Explanation

(i) `f(x) =2-3x,x inR,xfgt0`
Let `y=f(x)=2-3ximpliesy-2=-3x`
`implies" "3x=2-y" "impliesx=(2-y)/(3)`
`because" "xgt0," "therefore(2-y)/(3)gt`
`{:(implies,-ygt2),(implies,ylt2):}`
Therefore range of functio is `(0-oo,2].`
(ii) `f(x)=x^(2)+2,` x is a real number.
`{:(Let,y=f(x)),(therefore,y=x^(2)+2impliesx^(2)=y-2),(implies,x=sqrt(y-2)):}`
`therefore` x is a real number.
Therefore, range of function `=[2,oo).`
(iii) f(x) = x,x is a real number.
`Let" "y=f(x)impliesy=x`
`because` for each x,y is a real number.
Therefore, range = set of real numbers R.