Question

9. Analyze the following relations:

f: {1,3} →R, f(x) =
x 2
9:]-∞, 3[→ R, g(x) =
x+1
x² - 9
I
¿What of the following relations and functions ?
(A) only f
(B) only g
(C) both
(D) neither

Answer 1

After analyzing the provided relations, both f and g are functions as each element of their domains maps to exactly one element in the range, making option (C) both the correct choice.

Step-by-step explanation:

The question asks to analyze whether the given relations are functions. A function is a special kind of relation where each element in the domain is mapped to exactly one element in the range. Now let's examine each relation:

• For the relation f: {1,3} → R, f(x) is defined for each element in the domain {1,3}, mapping each to a unique real number. Therefore, f is indeed a function.
• For the relation g: ]-∞, 3[ → R, g(x) is the expression (x+1)/(x² - 9). Notice that the domain is all real numbers except 3, where the function would have a denominator of zero, which means it's undefined at x=3. However, for all other values within the domain, each x maps to exactly one value, making g a function as well.

Both relations meet the criteria for being functions since each element of their respective domains maps to exactly one element in the range without any ambiguity.

Therefore, the correct answer is (C) both.