Answer:
[tex]g(x) = 4^{x-1} + 3[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 4^x[/tex]
[tex]g(x) = f(x-1) + 3[/tex]
Required
Determine g(x)
First, we need to calculate f(x-1)
Given that:
[tex]f(x) = 4^x[/tex]
Subtract 1 from x
[tex]f(x-1) = 4^{x-1}[/tex]
Add 3 to both sides
[tex]f(x-1) + 3 = 4^{x-1} + 3[/tex]
Recall that:
[tex]g(x) = f(x-1) + 3[/tex]
This implies that:
[tex]g(x) = 4^{x-1} + 3[/tex]
