Answer:
[tex]f(x) = - \sqrt{x - a} + b[/tex]
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 [tex]\sqrt{x - a}[/tex]
So, there is only one function [tex]f(x) = - \sqrt{x - a} + b[/tex] ............ (1), that has the term [tex]\sqrt{x - a}[/tex] 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 [tex]f(x) = - \sqrt{x - a} + b[/tex]. (Answer)
