Question

Which of the following could be an example of a function with a range (-∞,a] and a domain [b, ∞) where a < 0 and b < 0?

Answer 1

Answer:

$f(x) = - \sqrt{x - b} + a$

Step-by-step explanation:

We have to choose the function from the given options which have a range (-∞, a] and a domain [b,∞) where a < 0 and b < 0.

I think the function is $f(x) = - \sqrt{x - b} + a$ ......... (1)

Here, x - b must be greater than equal to zero for the function to be real.

Hence, x - b ≥ 0

⇒ x ≥ b

So, the domain is [b, ∞).

Now, putting x = b in the equation (1),we get f(x) = a and putting x = ∞, we get f(x) = - ∞.

Therefore, the range of the function is (-∞, a]. (Answer)