Answer:
Reflection through y=x
Inverses
Step-by-step explanation:
Let's look at the graphs.
I'm going to point out some interesting things about the graphs.
You will see that (a,b) is a point on f while (b,a) is a point on g.
I'm using that [tex]f(x)=5^x[/tex] while [tex]g(x)=\log_5(x)[/tex].
You should see on the graph that:
[tex]f(1)=5^1=5[/tex] while [tex]g(5)=\log_5(5)=1[/tex]
See that (1,5) is on f while (5,1) is on g.
Let's look at another point:
[tex]f(0)=5^0=1[/tex] while [tex]g(1)=\log_5(1)=0[/tex]
See that (0,1) is on f while (1,0) is on g.
This relationship that they have is that they are inverses.
In general, the inverse of [tex]f(x)=a^x[/tex] is [tex]g(x)=\log_a(x)[/tex] and also vice versa.
Also visually, inverses when graphed will appear to be reflections through the y=x line.
