#### Question

Find the range of each of the following functions.

*f*(*x*) = 2 – 3*x*, *x* ∈ **R**, *x* > 0.

#### Solution

*f*(*x*) = 2 – 3*x*, *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

⇒ 3*x* > 0

⇒ 2 –3*x* < 2

⇒ *f*(*x*) < 2

∴Range of *f* = (–`oo`, 2)

Is there an error in this question or solution?

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