Question

The domain and range of the function \( f(x) = 2 - |x - 5| \) is

• A. Domain = \( \mathbb{R}^*, \) Range = \( (-\infty, 1] \)
• B. Domain = \( \mathbb{R}, \) Range = \( (-\infty, 2] \)
• C. Domain = \( \mathbb{R}, \) Range = \( [0, 2] \)
• D. Domain = \( \mathbb{R}, \) Range = \( (-\infty, 0] \)

Hint:

For absolute value functions, the domain is always \( \mathbb{R} \), and the range is determined by the maximum or minimum values of the expression.

Answer 1

The Correct Option is B

The function involves an absolute value, which is defined for all real numbers. The range is determined by the maximum value of \( 2 - |x - 5| \), which is \( (-\infty, 2] \).
Step 2: Conclusion.
The correct answer is (B), Domain = \( \mathbb{R}, \) Range = \( (-\infty, 2] \).