What is the relationship between a function and its inverse?
Practice Questions
Q1
What is the relationship between a function and its inverse?
They are always identical.
The inverse function undoes the action of the original function.
They can never intersect on a graph.
The inverse function is always a polynomial.
Questions & Step-by-Step Solutions
What is the relationship between a function and its inverse?
Step 1: Understand what a function does. A function takes an input and gives an output based on a specific rule.
Step 2: Learn about the inverse function. The inverse function takes the output of the original function and gives back the original input.
Step 3: Apply a function to an input. For example, if the function is f(x) = x + 2 and you input 3, the output is 5.
Step 4: Now apply the inverse function to the output. The inverse function of f(x) = x + 2 is f⁻¹(x) = x - 2. So, if you input 5 into the inverse function, you get back 3.
Step 5: Notice that applying the function and then its inverse returns you to the original input. This shows the relationship between a function and its inverse.
