Hello!
The answer is:
The function intercepts de x-axis at "x" equal to 1.631.
Why?
To find the x-intercept of the function, we need to make f(x) or "y" equal to 0, and then, isolate "x".
So, isolating we have:
[tex]f(x)=3^{(x-1)} -2\\\\0=3^{(x-1)} -2\\\\3^{(x-1)}=2\\\\Log_{3}(3^{(x-1)})=Log_{3}(2)\\\\x-1=0.631\\\\x=0.631+1=1.631[/tex]
Hence, we have that the function intercepts de x-axis at "x" equal to 1.631.
Have a nice day!
Note: I have attached a picture for better understanding.
