Question Find the excluded numbers from the domains of $f(x)=\sqrt{x}$ and $g(x)=\sqrt{x-2}$ by writing inequalities.

Studdy Solution

STEP 1

Assumptions
1. For a square root function to be real and defined, the argument (the expression inside the square root) must be greater than or equal to zero.
2. The domain of a function includes all the values of x for which the function is defined.

STEP 2

For the function $f(x)=\sqrt{x}$ , we need to find the values of $x$ that make the argument of the square root non-negative.
$x \geq 0$

STEP 3

The inequality that represents the numbers that must be excluded from the domain of $f(x)$ is therefore:
$x < 0$

STEP 4

For the function $g(x)=\sqrt{x-2}$ , we need to find the values of $x$ that make the argument of the square root non-negative.
$x - 2 \geq 0$

STEP 5

Solve the inequality to find the values of $x$ that are included in the domain.
$x \geq 2$

STEP 6

The inequality that represents the numbers that must be excluded from the domain of $g(x)$ is therefore:
$x < 2$
The numbers that must be excluded from the domain of each function are as follows: a) For $f(x)=\sqrt{x}$ , exclude $x < 0$ . b) For $g(x)=\sqrt{x-2}$ , exclude $x < 2$ .

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Question Find the excluded numbers from the domains of $f(x)=\sqrt{x}$ and $g(x)=\sqrt{x-2}$ by writing inequalities.

Studdy Solution

STEP 1

Assumptions
1. For a square root function to be real and defined, the argument (the expression inside the square root) must be greater than or equal to zero.
2. The domain of a function includes all the values of x for which the function is defined.

STEP 2

For the function $f(x)=\sqrt{x}$ , we need to find the values of $x$ that make the argument of the square root non-negative.
$x \geq 0$

STEP 3

The inequality that represents the numbers that must be excluded from the domain of $f(x)$ is therefore:
$x < 0$

STEP 4

For the function $g(x)=\sqrt{x-2}$ , we need to find the values of $x$ that make the argument of the square root non-negative.
$x - 2 \geq 0$

STEP 5

Solve the inequality to find the values of $x$ that are included in the domain.
$x \geq 2$

STEP 6

The inequality that represents the numbers that must be excluded from the domain of $g(x)$ is therefore:
$x < 2$
The numbers that must be excluded from the domain of each function are as follows: a) For $f(x)=\sqrt{x}$ , exclude $x < 0$ . b) For $g(x)=\sqrt{x-2}$ , exclude $x < 2$ .

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Question Find the excluded numbers from the domains of f(x)=xf(x)=\sqrt{x}f(x)=x​ and g(x)=x−2g(x)=\sqrt{x-2}g(x)=x−2​ by writing inequalities.

Studdy Solution

STEP 1

Assumptions1. For a square root function to be real and defined, the argument (the expression inside the square root) must be greater than or equal to zero.2. The domain of a function includes all the values of x for which the function is defined.

STEP 2

For the function f(x)=xf(x)=\sqrt{x}f(x)=x​, we need to find the values of xxx that make the argument of the square root non-negative.x≥0x \geq 0x≥0

STEP 3

The inequality that represents the numbers that must be excluded from the domain of f(x)f(x)f(x) is therefore:x<0x < 0x<0

STEP 4

For the function g(x)=x−2g(x)=\sqrt{x-2}g(x)=x−2​, we need to find the values of xxx that make the argument of the square root non-negative.x−2≥0x - 2 \geq 0x−2≥0

STEP 5

Solve the inequality to find the values of xxx that are included in the domain.x≥2x \geq 2x≥2

STEP 6

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Studdy solves anything!

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question Find the excluded numbers from the domains of $f(x)=\sqrt{x}$ and $g(x)=\sqrt{x-2}$ by writing inequalities.

Assumptions
1. For a square root function to be real and defined, the argument (the expression inside the square root) must be greater than or equal to zero.
2. The domain of a function includes all the values of x for which the function is defined.

For the function $f(x)=\sqrt{x}$ , we need to find the values of $x$ that make the argument of the square root non-negative.
$x \geq 0$

The inequality that represents the numbers that must be excluded from the domain of $f(x)$ is therefore:
$x < 0$

For the function $g(x)=\sqrt{x-2}$ , we need to find the values of $x$ that make the argument of the square root non-negative.
$x - 2 \geq 0$

Solve the inequality to find the values of $x$ that are included in the domain.
$x \geq 2$