Answer :
To find the value of [tex]\( f(21) \)[/tex] for the function [tex]\( f(x) = 4x^{-1} \)[/tex], follow these steps:
1. Understand the function: The function [tex]\( f(x) = 4x^{-1} \)[/tex] can be rewritten as [tex]\( f(x) = \frac{4}{x} \)[/tex]. This is because [tex]\( x^{-1} \)[/tex] is the same as [tex]\(\frac{1}{x}\)[/tex].
2. Substitute the value: We need to find [tex]\( f(21) \)[/tex]. So, substitute [tex]\( x = 21 \)[/tex] into the function:
[tex]\[
f(21) = \frac{4}{21}
\][/tex]
3. Evaluate the expression: Calculate the value of [tex]\( \frac{4}{21} \)[/tex].
[tex]\[
\frac{4}{21} \approx 0.1905
\][/tex]
This result matches the decimal approximation given. Therefore, the value of [tex]\( f(21) \)[/tex] is [tex]\( \frac{4}{21} \)[/tex].
Based on the options provided, the correct answer is:
[tex]\[ \text{(C) } \frac{4}{21} \][/tex]
1. Understand the function: The function [tex]\( f(x) = 4x^{-1} \)[/tex] can be rewritten as [tex]\( f(x) = \frac{4}{x} \)[/tex]. This is because [tex]\( x^{-1} \)[/tex] is the same as [tex]\(\frac{1}{x}\)[/tex].
2. Substitute the value: We need to find [tex]\( f(21) \)[/tex]. So, substitute [tex]\( x = 21 \)[/tex] into the function:
[tex]\[
f(21) = \frac{4}{21}
\][/tex]
3. Evaluate the expression: Calculate the value of [tex]\( \frac{4}{21} \)[/tex].
[tex]\[
\frac{4}{21} \approx 0.1905
\][/tex]
This result matches the decimal approximation given. Therefore, the value of [tex]\( f(21) \)[/tex] is [tex]\( \frac{4}{21} \)[/tex].
Based on the options provided, the correct answer is:
[tex]\[ \text{(C) } \frac{4}{21} \][/tex]
