Domain and Range of Functions

The video tutorial by C chamber Jacob explains how to find the domain and range of the function f(x) = √(2 - x). The domain is determined by ensuring the expression under the square root is non-negative, resulting in x being less than or equal to 2. The range is found by evaluating the smallest and largest possible values of the function, leading to f(x) being greater than or equal to 0. The video concludes with a brief mention of the next tutorial in the series.

What is the function given in the video for which the domain and range need to be found?

• f(x) = 2x - 1

• f(x) = x^2 + 2

• f(x) = √(2 - x)

• f(x) = 1/(x - 2)

How do you find the domain of the function f(x) = √(2 - x)?

• By setting 2 - x > 0

• By setting 2 - x = 0

• By setting x^2 - 2 = 0

• By setting x + 2 = 0

Why are numbers greater than 2 not included in the domain of f(x) = √(2 - x)?

• They result in a negative number under the square root.

• They make the function undefined.

• They result in a zero under the square root.

• They make the function equal to zero.

What is the domain of the function f(x) = √(2 - x) in interval notation?

• [0, 2]

• (-∞, 2)

• [2, ∞)

• (-∞, 2]

What is the smallest value of f(x) = √(2 - x) when x is in its domain?

• 2

• 1

• -1

• 0

What is the range of the function f(x) = √(2 - x)?

• (-∞, 0]

• (-∞, 2]

• [2, ∞)

• [0, ∞)

If x = 1, what is the value of f(x) = √(2 - x)?

• -1

• 2

• 0

• 1

What happens if you substitute x = 3 into the function f(x) = √(2 - x)?

• The result is an imaginary number.

• The result is a positive number.

• The result is zero.

• The result is undefined.

What is the value of f(x) = √(2 - x) when x = 0?

• 1

• 2

• 0

• √2

Which of the following values of x is not in the domain of f(x) = √(2 - x)?

• 3

• -1

• 1

• 0