Question

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

Write the new equation for g.
G=

Answer 1

`g(x) = 4^(x-1) + 3`

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`