Understanding the Function f(x) = √(2 - x)

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 value of the function, which is zero, and determining that f(x) is greater than or equal to zero. The video concludes with a prompt to watch the next video for further learning.

What is the function given in the video?

• f(x) = √(2 - x)

• f(x) = 2x - √x

• f(x) = √(x - 2)

• f(x) = x² - 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 = 0

• By setting x > 2

Why can't x be greater than 2 in the domain of f(x) = √(2 - x)?

• Because it results in a positive number

• Because it results in a negative number

• Because it results in zero

• Because it results in an imaginary number

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

• (-∞, 2)

• [2, ∞)

• [0, 2]

• (-∞, 2]

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

• 1

• -1

• 0

• 2

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

• (-∞, 2]

• [0, ∞)

• (-∞, 0]

• [0, 2]

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

• √2

• 1

• 0

• 2

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

• You get an imaginary number

• You get a negative number

• You get zero

• You get a positive number

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

• √2

• 2

• 1

• 0

Which of the following is not a valid x-value for the domain of f(x) = √(2 - x)?

• 1

• 0

• 3

• 2