Answer:
f(-2) = 5/9
Step-by-step explanation:
* lets explain the problem
∵ f(x) = 5(3)^x
- It is an exponential function
- (3) is the base of the function
- x is the exponent
- To find f(-2) means substitute x by -2
∵ [tex]f(x)=5(3)^{x}[/tex]
∵ x = -2
∴ [tex]f(-2)=5(3)^{-2}[/tex]
- If the power of the base is negative we can change its sign to
positive by reciprocal the base
# Ex: [tex](a)^{-n}=(\frac{1}{a})^{n}[/tex]
- Lets do that withe the base 3 and power -2
∵ [tex](3)^{-2}=(\frac{1}{3})^{2}[/tex]
∴ [tex]f(-2)=5(\frac{1}{3})^{2}=5(\frac{1}{9})=\frac{5}{9}[/tex]
* f(-2) = 5/9
