Question

The domain and range of the function f given by f (x) = 2 – |x −5| is

A. Domain = R⁺, Range = ( – ∞, 1]
B. Domain = R, Range = ( – ∞, 2]
C. Domain = R, Range = (– ∞, 2)
D. Domain = R⁺, Range = (– ∞, 2]

Answer 1

Given: f(x) = 2–|x −5|

To find: the domain and range of function

Explanation: So the domain of a function consists of all the first elements of all the ordered pairs, i.e., x, so we have to find the values of x to get the required domain

Given,

f(x) = 2–|x −5|

Now x is defined for all real numbers

Hence the domain of f is R

And the range of a function consists of all the second elements of all the ordered pairs, i.e., f(x), so we have to find the values of f(x) to get the required range

Now we know

|x-5|≥0

or

-|x-5|≤0

Adding 2 we get

2-|x-5|≤2

⇒ f(x)≤2

Hence the range of f = (-∞, 2]

Hence the correct answer is option (B)