Answer :
We are given a function f ( x ) defined as follows:
[tex]y=f(x)=x^{\frac{1}{9}}[/tex]We are to determine the value of f ( x ) when,
[tex]\times\text{ = }\frac{1}{2}[/tex]In such cases, we plug in/substitue the given value of x into the expressed function f ( x ) as follows:
[tex]y\text{ = f ( }\frac{1}{2}\text{ ) = (}\frac{1}{2})^{\frac{1}{9}}[/tex]We will apply the power on both numerator and denominator as follows:
[tex]f(\frac{1}{2})=\frac{1^{\frac{1}{9}}}{2^{\frac{1}{9}}}\text{ = }\frac{1}{2^{\frac{1}{9}}}[/tex]Now we evaluate ( 2 ) raised to the power of ( 1 / 9 ).
[tex]f\text{ ( }\frac{1}{2}\text{ ) = }\frac{1}{1.08005}[/tex]Next apply the division operation as follows:
[tex]f\text{ ( }\frac{1}{2})\text{ = }0.92587[/tex]Once, we have evaluated the answer in decimal form ( 5 decimal places ). We will round off the answer to nearest thousandths.
Rounding off to nearest thousandth means we consider the thousandth decimal place ( 3rd ). Then we have the choice of either truncating the decimal places ( 4th and onwards ). The truncation only occurs when (4th decimal place) is < 5.
However, since the (4th decimal place) = 8 > 5. Then we add ( 1 ) to the 3rd decimal place and truncate the rest of the decimal places i.e ( 4th and onwards ).
The answer to f ( 1 / 2 ) to the nearest thousandth would be:
[tex]\textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( }}\textcolor{#FF7968}{\frac{1}{2})}\text{\textcolor{#FF7968}{ = 0.926}}[/tex]
