Question

Which function has a domain of x greater-than-or-equal-to 5and a range of y less-than-or-equal-to 3?.

Answer 1

Function's domain is the set of values on which it is defined. One such function having domain x≥ 5 and range y ≤ 3 is: $y = 3 - \sqrt{x-5}$

What is domain and range of a function?

• Domain is the set of values for which the given function is defined.
• Range is the set of all values which the given function can output.

There can be actually infinite functions having same domain and range.

We need to find one function whose domain is x≥ 5 and range is y ≤ 3

Let the function be $y = f(x)$

For keeping the function not defined for values of x < 5, we need to make such condition such that for values x < 5, the values of the function becomes undefined.

We can use some trick which keeps one sided interval undefined. One such function is the square root function which needs the input to be non-negative,

If we input x-5 to the square root function, then x can't go below 5, as square root of negative values is not defined(if not using complex numbers).

Thus, $\sqrt{x-5}$ is one part of f(x).

Next, we need the output to be limited by 3.

Since the quantity  $\sqrt{x-5}$  is never negative, so 3 -  $\sqrt{x-5}$  is never going to be bigger than 3.

Thus, $y = 3 - \sqrt{x-5}$ is one such needed function, having domain x≥ 5 and range y ≤ 3

Learn more about domain and range here:

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