Question

Select each pair of functions that are inverses of each other. f (x) = left-brace (negative 5, negative 9), (negative 3, negative 4), (0, 1), (3, 7), (6, 13) right-brace. G (x) = left-brace (negative 9, negative 5), (negative 4, negative 3), (1, 0), (7, 3), (13, 6), right-brace. f (x) = x + 7; g (x) = x minus 7 2 2-column tables with 4 rows. Table 1 is titled f (x). Column 1 is labeled x with entries 2, 3, 4, 5. Column 2 is labeled y with entries 3, 8, 15, 24. Table 2 is titled g (x). Column 1 is labeled x with entries 5, 4, 3, 2. Column 2 is labeled y with entries 24, 15, 8, 3.

Answer 1

look at the image :)

Answer 2

The first two pairs of functions are inverse of each other

Explanation:

Inverse functions?

1...................................

f(x) = {(-5, -9), (-3, -4), (0,1), (3,7), (6,13)}

g(x) = {(-9,-5), (-4, -3), (1,0), (7,3), (13,6)}

• Yes, this pair is inverse as all points of the functions have inverse values

2...................................

f(x) = x + 7 is given

Inverse of f(x) is

• x = f'(x) + 7 ⇒ f'(x) = x - 7

Since g(x) = x - 7 it is inverse with f(x)

• Yes, this pair is inverse as described above

3...................................

Data of f(x) and g(x)

x = {2, 3, 4, 5} f(x) = {3, 8, 15, 24}

x = {5, 4, 3, 2} g(x) = {24, 15, 8, 3}

• No, as both functions have same domain and range

• example is f(2) = 3 and g(2) = 3 as per table