Graph both functions. Can you relate one to the other in a specific way?
See solution.
Practice makes perfect
We can start by graphing both functions to compare them, but first let us label them so that we can differ between each of them.
y_1=log_3(x+1) y_2 = 3^x-1
Notice that the function y_1 is a reflection of y_2 across the line y=x. For a clearer visualization of this we can graph them again together with the line y=x, and localize a pair of points in one of the functions. The points with the coordinates swapped should be part of the other graph.
As the graphs have the properties described above, for each pair of values the input of one function is the output of the other, and vice-versa. Therefore, this pair of functions are inverse functions. We can also note this by analyzing their domain, range, and asymptotes. We will summarize this information using a table.
y_1= log_3 (x+1)
y_2=3^x-1
y_1 is the inverse of y_2. Therefore, its graph is the reflection of the graph of y_2 across the line y=x.
