AnswersPrecalculusComparing a Function and Its Inverse — QuizQuestion 25
25
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Comparing a Function and Its Inverse — Quiz

Question 25 • Precalculus

A linear function and its inverse are given. y is equal to 4 x minus 3 and y is equal to 1 fourth x plus 3 fourths Which tables could be used to verify that the functions are inverses of each other? Choose two correct answers.

Answer
A
Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 18'; Column 3, 'negative 12'; Column 4, '0'; Column 5, '3'; Column 6, '9' Row 2: Column 1, 'y'; Column 2, 'negative 24'; Column 3, 'negative 18'; Column 4, 'negative 6'; Column 5, 'negative 3'; Column 6, '3'
B
Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 23'; Column 3, 'negative 15'; Column 4, 'negative 3'; Column 5, '1'; Column 6, '13' Row 2: Column 1, 'y'; Column 2, 'negative 5'; Column 3, 'negative 3'; Column 4, '0'; Column 5, '1'; Column 6, '4'
C
Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 5'; Column 3, 'negative 3'; Column 4, '0'; Column 5, '1'; Column 6, '4' Row 2: Column 1, 'y'; Column 2, 'negative 23'; Column 3, 'negative 15'; Column 4, 'negative 3'; Column 5, '1'; Column 6, '13'
D
Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, 'negative 24'; Column 3, 'negative 18'; Column 4, 'negative 6'; Column 5, 'negative 3'; Column 6, '3' Row 2: Column 1, 'y'; Column 2, 'negative 18'; Column 3, 'negative 12'; Column 4, '0'; Column 5, '3'; Column 6, '9'
E
Table with 6 columns and 2 rows.Row 1: Column 1, 'x'; Column 2, '1'; Column 3, '3'; Column 4, '5'; Column 5, '7'; Column 6, '9' Row 2: Column 1, 'y'; Column 2, '1'; Column 3, '3'; Column 4, '5'; Column 5, '7'; Column 6, '9'

Explanation

For y = 4x − 3, substituting x = −5, −3, 0, 1, and 4 gives y = −23, −15, −3, 1, and 13. Those pairs appear in table C. An inverse swaps each input and output, so its table should pair −23 with −5, −15 with −3, and so on; those pairs appear in table B. Tables A and D do not follow the given functions.

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