Use composition of functions to determine whether and are inverses of one another.

Question

Use composition of functions to determine whether  and  are inverses of one another.

Quizplus · Accepted Answer

To check for inverse functions, we need to check if the composition of the two functions results in the identity function.

Let f(x) = 11ebfdc1_ec2e_882d_abe3_75e6a8f7b6e5_TBX8727_11 and g(x) = 11ebfdc1_ec2e_882e_abe3_69a2c9a36a58_TBX8727_11.

f(g(x)) = f(11ebfdc1_ec2e_882e_abe3_69a2c9a36a58_TBX8727_11) = 11ebfdc1_ec2e_882d_abe3_75e6a8f7b6e5_TBX8727_11
g(f(x)) = g(11ebfdc1_ec2e_882d_abe3_75e6a8f7b6e5_TBX8727_11) = 11ebfdc1_ec2e_882e_abe3_69a2c9a36a58_TBX8727_11

Since f(g(x)) = g(f(x)) = x, we can conclude that the functions are inverses of each other. Hence, the answer is A.

Use Composition of Functions to Determine Whether and