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Question
Find the range of the following function.
f(x) = 2 – 3x, x ∈ R, x > 0.
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Solution
Given: f(x) = 2 – 3x, x ∈ R, x > 0
The values of f(x) for various values of real numbers x > 0 can be written in the tabular form as
| x | 0.01 | 0.1 | 0.9 | 1 | 2 | 2.5 | 4 | 5 | ... |
| f(x) | 1.97 | 1.7 | -0.7 | -1 | -4 | -5.5 | -10 | -13 | ... |
Thus, it can be clearly observed that the range of f is the set of all real numbers less than 2.
i.e., range of f = (–`oo`, 2)
Alter:
Let x > 0
⇒ 3x > 0
⇒ 2 –3x < 2
⇒ f(x) < 2
∴ Range of f = (–`oo`, 2)
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