Question

let f : R to R define f(x)=x+5.find it's domain n range
​

Answer 1

Domain, basically, is the set of all those values for which the function is defined or in other words, the function doesn't take any absurd form.

Since, the function f(x) = x + 5 is defined for all real values of x, thereby, it's domain is the set of all real numbers, i.e., it's domain is R.

=> Domain of f(x) = R = (-∞, ∞).

Now, the range of the function is the set of value of f(x) at the points where x is defined. That is,

Range = {y : y = f(x), x is defined}

Here, the function is f(x) = x + 5. For time being, let f(x) = y.

f(x) = y = x + 5

=> x = y - 5

The function, x = y - 5, is defined for all real values of y, thereby, y can take any real value ranging from -∞ to ∞ or from (-∞, ∞).

Hence, y belongs to R = (-∞, ∞)

Therefore, range of function is the set of all real numbers.

=> Range of f(x) = R = (-∞, ∞).

Hence,

• Domain of f(x) = R = (-∞, ∞).
• Range of f(x) = R = (-∞, ∞).