Answer:
[tex]k(x)=2^{x}[/tex] ⇒ 1st answer
Step-by-step explanation:
* Lets explain how to solve the problem
∵ [tex]g(x)=3(2^{x})[/tex]
∵ [tex]h(x)=2^{x+1}[/tex]
- Lets revise this rule to use it
# If [tex]a^{n}*a^{m}=a^{n+m}====then==== a^{n+m}=a^{n}*a^{m}[/tex]
- We will use this rule in h(x)
∵ [tex]h(x)=2^{x+1}[/tex]
- Let a = 2 , n = x , m = 1
∴ [tex]h(x)=2^{x}*2^{1}[/tex]
- Now lets find k(x)
∵ k(x) = (g - h)(x)
∵ [tex]g(x)=3(2^{x})[/tex]
∵ [tex]h(x)=2^{x}*2^{1}[/tex]
∴ [tex]k(x)=3(2^{x})-(2^{x}*2^{1})[/tex]
- We have two terms with a common factor [tex]2^{x}[/tex]
∵ [tex]2^{x}[/tex] is a common factor
∵ [tex]\frac{3(2^{x})}{2^{x}}=3[/tex]
∵ [tex]\frac{2^{x}*2^{1}}{2^{x}}=2^{1}=2[/tex]
∴ [tex]k(x) = 2^{x}[3 - 2]=2^{x}(1)=2^{x}[/tex]
* [tex]k(x)=2^{x}[/tex]
