Answer:
[tex]f(x) = 2[\frac{3^x}{9}] + 2[/tex]
[tex]f(x) = 8(4)^x[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 2(3)^{x-2} + 2[/tex]
[tex]f(x) = \frac{1}{2}(4)^{x+2}[/tex]
Required
Remove the h component
In a function, the h component is highlighted as:
[tex]f(x) = a^{x+h}[/tex]
So, we have:
[tex]f(x) = 2(3)^{x-2} + 2[/tex]
Split the exponents using the following law of indices:
[tex]a^m/a^n = a^{m-n}[/tex]
[tex]f(x) = 2*\frac{3^x}{3^2} + 2[/tex]
[tex]f(x) = 2*\frac{3^x}{9} + 2[/tex]
[tex]f(x) = 2[\frac{3^x}{9}] + 2[/tex]
The h component has been removed
[tex]f(x) = \frac{1}{2}(4)^{x+2}[/tex]
Split the exponent using the following law of indices
[tex]a^{m+n} =a^m * a^n[/tex]
So, we have:
[tex]f(x) = \frac{1}{2}(4)^x * 4^2[/tex]
Express 4^2 as 16
[tex]f(x) = \frac{1}{2}(4)^x * 16[/tex]
Divide 16 by 2
[tex]f(x) = 8(4)^x[/tex]
