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?

a)f(x)= √x+a -b

b) f(x)= -√x-a +b

c)f(x)= 3√x+a -b

d) f(x)= ^3√(x-b) +a

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

So, there is only one function ............ (1), that has  the term 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 . (Answer)

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.