Answer:
The answer is given below
Step-by-step explanation:
Given that:
[tex]f(x)=\frac{1}{3}(81)^ \frac{3x}{4} \\Using\ exponent\ rule:a^{xy}=a^xa^y\\f(x)=\frac{1}{3}(81^{1/4})^ {3x}\\f(x)=\frac{1}{3}(3})^ {3x}\\f(x)=\frac{(3)^ {3x}}{3^1} \\Using\ exponent\ rule:a^x/a^y=a^{x-y}\\f(x)=3^ {3x-1}[/tex]
The function is an exponential function.
The domain is the set of all independent variables i.e the input values (x values). For an exponential function, the domain is the set of all real numbers. That is:
Domain: x = (-ā, ā)
The range is the set of all dependent variables i.e the values of y. For an exponential function, the range is the set of all real numbers greater than zero. That is:
Range: y = (0, ā)
Answer:
initial value 1/3
simplified base 27
domain is all real numbers
range is y>0
Step-by-step explanation:
