What is the domain and range of the function f(x) = 3x + 5?

Solution:

Given, f(x) = 3x + 5

Clearly no real value of f(x) can make f(x) an imaginary value or value like ∞.

Domain = R or (-∞, ∞)

Range = R, because ∀ x ∈ R(Domain) f(x) is also real.

The domain and range can be observed from the following graph:

As we observe, lines go off infinitely in both directions.

Therefore, the domain and range of this function are both set of reals or (-∞, ∞).

Example:

Suppose f(x) = 1/x

When x = 0, f(x) = 1/0 = infinity

Thus, the domain of f(x) cannot be R. Therefore, to define the domain the values of x which make f(x) = infinity are excluded from the set of reals.

Therefore the domain is R - {0}.

What is the domain and range of the function f(x) = 3x + 5?

Summary:

The domain and range of this function are both set of reals or (-∞, ∞).