Question

Let f(x)=4^x. The new function g(x)=f(x-1)+3 represents transformations that were made to function f.

Answer 1

Answer:

$g(x) = 4^{x-1} + 3$

Step-by-step explanation:

Given

$f(x) = 4^x$

$g(x) = f(x-1) + 3$

Required

Determine g(x)

First, we need to calculate f(x-1)

Given that:

$f(x) = 4^x$

Subtract 1 from x

$f(x-1) = 4^{x-1}$

Add 3 to both sides

$f(x-1) + 3 = 4^{x-1} + 3$

Recall that:

$g(x) = f(x-1) + 3$

This implies that:

$g(x) = 4^{x-1} + 3$