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Graphing a Radical Function

The domain of [tex]y=\sqrt{x-5}-1[/tex] is


Sagot :

To find the domain of the function [tex]\( y = \sqrt{x - 5} - 1 \)[/tex], we need to ensure that the expression inside the square root is non-negative because the square root function is only defined for non-negative values (i.e., the radicand must be greater than or equal to zero).

Here's a step-by-step solution:

1. Identify the radicand:
The radicand is the expression inside the square root, which in this case is [tex]\( x - 5 \)[/tex].

2. Set the radicand greater than or equal to zero:
For the square root function to be defined, we need:
[tex]\[ x - 5 \geq 0 \][/tex]

3. Solve the inequality:
To find the values of [tex]\( x \)[/tex] that satisfy the inequality [tex]\( x - 5 \geq 0 \)[/tex], we add 5 to both sides:
[tex]\[ x \geq 5 \][/tex]

4. Write the domain:
The solution to the inequality [tex]\( x \geq 5 \)[/tex] represents the domain of the function [tex]\( y = \sqrt{x - 5} - 1 \)[/tex]. This means the function is defined for all [tex]\( x \)[/tex] values that are greater than or equal to 5.

Therefore, the domain of [tex]\( y = \sqrt{x - 5} - 1 \)[/tex] is:

[tex]\[ x \geq 5 \][/tex]