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# Find The Range of Each of the Following Functions. F(X) = 2 – 3x, X ∈ R, X > 0. - CBSE (Arts) Class 11 - Mathematics

ConceptSome Functions and Their Graphs

#### Question

Find the range of each of the following functions.

f(x) = 2 – 3xx ∈ Rx > 0.

#### Solution

f(x) = 2 – 3xx ∈ Rx > 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)

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 11 (2018 to Current)
Chapter 2: Relations and Functions
Ex. 2.30 | Q: 5.1 | Page no. 44

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Solution Find The Range of Each of the Following Functions. F(X) = 2 – 3x, X ∈ R, X > 0. Concept: Some Functions and Their Graphs.
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