1. ## Inverse Functions

For a lot of explanations for why something is an inverse function, my textbook will say

"For each value of x only one value of y can be calculated, therefore, the inverse is a function"

But how can you tell that

y=(x+4)/3

only has one value of y for every value of x without testing it out a million times?

2. Originally Posted by juliak
For a lot of explanations for why something is an inverse function, my textbook will say

"For each value of x only one value of y can be calculated, therefore, the inverse is a function"

But how can you tell that

y=(x+4)/3

only has one value of y for every value of x without testing it out a million times?
graph the original function and see if it passes the horizontal line test ... if any horizontal line intersects the graph of $\displaystyle f(x)$ only once, then its inverse $\displaystyle f^{-1}(x)$ is also a function.

3. Is there any where to tell without graphing the equation?

4. Originally Posted by juliak
Is there any where to tell without graphing the equation?
you can find the inverse itself and and determine if it is a function.