174k views
1 vote
Look at the function you wrote for question 5. does this function have an inverse? if so, what is it? is the inverse a function? show your work and explain your reasoning.

User Sport
by
7.9k points

1 Answer

5 votes

Final answer:

To determine if a function has an inverse, check if it passes the horizontal line test and if it is defined. To find the inverse, interchange the x and y variables and solve for y. If the original function passes the vertical line test, then the inverse is also a function.

Step-by-step explanation:

The function in question 5 would need to be defined in order to determine if it has an inverse. Assuming the function is defined, we can determine if it has an inverse by checking if it passes the horizontal line test. If for every y-value, there is only one x-value, then the function has an inverse. To find the inverse, we can interchange the x and y variables and solve for y.

If the inverse is also a function depends on whether the original function passes the vertical line test as well. If for every x-value, there is only one y-value, then both the function and its inverse are functions.

User Alex Grande
by
7.7k points