Inequalities and Function Domains

The video tutorial explains how to find the domain of square root functions by ensuring the expression under the square root is non-negative. It provides examples with different expressions, demonstrating how to set up and solve inequalities to determine valid X values. Key points include handling negative coefficients and remembering to flip inequalities when dividing by a negative number.

Why is it important to ensure non-negative values under a square root?

• To make calculations easier

• To ensure the function is defined

• To simplify the function

• To avoid complex numbers

What is the domain of the function f(x) = √x?

• x ≥ 0

• x > 0

• x ≤ 0

• x < 0

How do you set up an inequality for the function f(x) = √(8 + x)?

• 8 + x ≤ 0

• 8 + x < 0

• 8 + x > 0

• 8 + x ≥ 0

What is the domain of the function f(x) = √(8 + x)?

• x ≤ -8

• x < -8

• x ≥ -8

• x > -8

Why is it incorrect to assume all negative numbers are invalid under a square root?

• Because the square root of a negative number is always positive

• Because some negative numbers can be squared

• Because adding a positive number can make the result non-negative

• Because negative numbers are not real

What is the domain of the function f(x) = √(x + 8)?

• x > -8

• x ≥ -8

• x < -8

• x ≤ -8

What is the domain of the function f(x) = √(3x + 9)?

• x > -3

• x ≥ -3

• x < -3

• x ≤ -3

What is the domain of the function f(x) = √(5x + 25)?

• x ≤ -5

• x < -5

• x ≥ -5

• x > -5

What is the domain of the function f(x) = √(7x + 49)?

• x > -7

• x ≥ -7

• x < -7

• x ≤ -7

What is the domain of the function f(x) = √(10x + 100)?

• x > -10

• x < -10

• x ≥ -10

• x ≤ -10