Question

Select the correct answer from given alternative.

The domain and range of f(x) = 2 − |x − 5| is

Options

• R⁺, `(- ∞, 1]`

• R, `(- ∞, 2]`

• R, `(- ∞, 2)`

• R⁺, `(- ∞, 2]`

Answer 1

R, `(- ∞, 2]`

Explanation;

f(x) = 2 − |x − 5|

= 2 – (5 – x), x < 5

= 2 – (x – 5), x ≥ 5

∴ f(x) = `{(x - 3","  x < 5),(7 - x","  x ≥ 5):}`

 Domain = R,

Range (from graph) = `(- ∞, 2]`