Question -
Answer -
(i) Given,
f(x) = 2 – 3x, x ∈ R, x > 0.
We have,
x > 0
So,
3x > 0
-3x < 0 [Multiplying by -1 both the sides, the inequality sign changes]
2 – 3x < 2
Therefore, the value of 2 – 3x is less than 2.
Hence, Range = (–∞, 2)
(ii) Given,
f(x) = x2 + 2, x is a real number
We know that,
x2 ≥ 0
So,
x2 + 2 ≥ 2 [Adding 2 both the sides]
Therefore, the valueof x2 + 2 is always greater or equal to 2 for x isa real number.
Hence, Range = [2, ∞)
(iii) Given,
f(x) = x, x is a realnumber
Clearly,the range of f is the set of all real numbers.
Thus,
Range of f = R