1)Initial value of the function is 1/2.
2)The domain and range of the function are R and R⁺ respectively.
The given function is:
[tex]f(x) =\frac{1}{2} 27^{\frac{2x}{3} }[/tex]
The given function can be written as
[tex]f(x) =\frac{1}{2} (3^3)^{\frac{2x}{3} }[/tex]
[tex]f(x)=\frac{1}{2} 9^{x}[/tex] which is an exponential function.
What is an exponential function?
A function of the form [tex]y=ab^x[/tex]exponential function where [tex]b\neq 1[/tex].
Initial value f(0) = 1/2
We know the domain of an exponential function is a set of all real numbers or R or [tex](-\infty,+\infty)[/tex].
The range of an exponential function is a set of all positive real numbers or R⁺ or [tex](0,+\infty)[/tex].
Hence, 1)Initial value of the function is 1/2.
2)The domain and range of the function are R and R⁺ respectively.
To get more about domain and range visit:
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