Question

select the correct answer. this table defines a function.

x	7	10	13	16
y	21	30	39	48

which table represents the inverse of the function defined above?
a.

x	7	10	13	16
y	-21	-30	-39	-48

b.

x	-7	-10	-13	-16
y	21	30	39	48

c.

x	21	30	39	48
y	7	10	13	16

d.

x	-21	-30	-39	-48
y	7	10	13	16

Explanation:

Step1: Recall inverse function definition

To find the inverse of a function defined by a table, we swap the \( x \) and \( y \) values. The original function has pairs \((7, 21)\), \((10, 30)\), \((13, 39)\), \((16, 48)\).

Step2: Swap x and y for each pair

For the inverse function, the pairs should be \((21, 7)\), \((30, 10)\), \((39, 13)\), \((48, 16)\). We check the options:

• Option A: Keeps \( x \) as 7,10,13,16 and negates \( y \) – incorrect.
• Option B: Negates \( x \) and keeps \( y \) – incorrect.
• Option C: Has \( x \) as 21,30,39,48 (original \( y \) values) and \( y \) as 7,10,13,16 (original \( x \) values) – matches the swapped pairs.
• Option D: Negates \( x \) (original \( y \) values negated) and keeps \( y \) as original \( x \) – incorrect.

Answer:

C.

x	21	30	39	48