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Question -

Find the range of each of the following functions.
(i) f(x) = 2 – 3x, x ∈ R, x > 0.
(ii) f(x) = x2 + 2, x is a real number.
(iii) f(x) = x, x is a real number.



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

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