Question

The inverse of a function exists if the function is
a) one to one
b) onto
c) one to one and onto
d) into ​

Answer 1

An inverse of a function exists when the result is unique in its image . An example of a function that has unique results, regardless of the input is the following: What it means to be unique is that for each x, there is only one f(x) value. Another example is the square.

Answer 2

a)The inverse function exists in one to one function.

Explanation:

• The inverse function is inversed using one to one or it will go by the horizonal line (x).
• Consider f and g be two functions we get  $f(g(x))=x$ and $g(f(x))=x$ .
• In this case, the function of g is the inverse function of f. So, we get $f(f^{-1}(x))=x$  and $f^{-1}(f(x))=x$.
• Here the range and domain of the function f will be same.
• One to one function means there is no repeated values of y.