Question

2. “The inverse of every function must be a function itself.” State whether you agree or disagree with the statement providing evidence to support your position.

Answer 1

A function that is its own inverse is called  a involution. It is not necessary the inverse of every function must be a function itself.”

Step-by-step explanation:

Inverse is a function that reverse itself

Lets ,consider an equation  used to convert temperature in degrees Fahrenheit( F), to a temperature in degrees Celsius,(C)

C=3/9(F-32)

​But suppose ,we want a equation that did the reverse  that means it converted a temperature in degrees Celsius to a temperature in degrees Fahrenheit. Then we inverse the function as

F=3/9(C+32)

Answer 2

Technically this is not necessarily true for all. A function has each input mapped to one output, therefore there can be two inputs that have the same output. However, when inverted, the input will have two outputs, which is not a function. For example with (1,3) (2,3) (3,4) (4,5) this is a function but switched (3,1) (3,2) ! Two inputs have the same output, which is not a function!