Question

Domain of the function f(x) = 6 -|x -3| is

Answer 1

Concept

The set of all values for which a function is defined is known as its domain, and the set of all values that the function can accept is known as its range.

Given

Function f(x) = 6 ₋ I x ₋ 3 I

Find

The domain of the function.

Solution

In order to obtain the necessary range, we must discover the values of the function f(x), whose domain is all of the initial elements of all ordered pairs.

f(x) = 6 ₋ I x ₋ 3 I

Now x is defined for all real numbers.

Hence the domain of f is R.

And a function's range is made up of all the second elements of all ordered pairs, or f(x), therefore we must determine the values of f(x) to obtain the necessary range.

let,

x = ₋2

then, 6 ₋ I ₋2 ₋ 3 I = 6 ₋ I ₋5 I

                            = 11

for x = 8

6 ₋ I 8 ₋ 3 I = 6 ₋ I ₋2 I

                 = 3

Therefore we can notice that x ∈ R. which means x contains all real numbers.

Hence domain of the function f(x) = 6 -|x -3| is (₋∞ , ₊∞)

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