Question

Find the range of each of the following functions. (i) f ( x ) = 2 – 3 x , x ∈ R , x > 0. (ii) f ( x ) = x 2 + 2, x , is a real number. (iii) f ( x ) = x , x is a real number

Answer 1

(i)

Given function is,

f( x )=2−3x, x∈R, x>0

For the relation,

x>0 (1)

Multiply 3 on both sides of the equation (1).

3x>0 (2)

Multiply ( −1 ) on both sides of the equation (2).

−3x<0 (3)

Add 2 on both sides of the equation (3).

2−3x<2+0 f( x )<2

Hence, the range of the function is ( −∞, 2 ) .

(ii)

Square both sides of the equation (1), which makes it positive or 0 .

x 2 ≥0 (4)

Add 2 on both sides of the equation (4).

x 2 +2≥2 f( x )≥2

Hence, the range of the function is [ 2, ∞ ) .

(iii)

Given function is,

f( x )=x    x∈R

Hence, the range of the function is, f( x )=R .