Question

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

Answer 1

Answer:

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

Step-by-step explanation:

We are given a few functions in options and we have to choose from them that has the domain [a,∞) and range (-∞,b].

Now, for domain i.e. the value of x ≥ a.

Therefore, the value of y must be a function of $\sqrt{x - a}$

So, there is only one function $f(x) = - \sqrt{x - a} + b$ ............ (1), that has  the term $\sqrt{x - a}$ in it.

Now, for x = a, the value of f(x) becomes b and for x = ∞ the function f(x) value becomes -∞.

Therefore, the range of the function will be (-∞,b] i.e. y ≤ b.  

Hence, the required function is $f(x) = - \sqrt{x - a} + b$. (Answer)