Question

multiple choice. choose the one alternative that best completes the statement or answers the question. evaluate the function at the given value of the independent variable and simplify. 30) f(x) = \frac{x^{3}+3}{x^{2}-5}; f(5) a) \frac{25}{4} b) \frac{32}{5} c) \frac{7}{5} d) \frac{128}{5} short answer. write the

Explanation:

Step1: Substitute x = 5 into the function

Substitute \(x = 5\) into \(f(x)=\frac{x^{3}+3}{x^{2}-5}\), we get \(f(5)=\frac{5^{3}+3}{5^{2}-5}\).

Step2: Calculate the numerator

Calculate \(5^{3}+3\): \(5^{3}=5\times5\times5 = 125\), so \(5^{3}+3=125 + 3=128\).

Step3: Calculate the denominator

Calculate \(5^{2}-5\): \(5^{2}=25\), so \(5^{2}-5=25 - 5 = 20\).

Step4: Simplify the fraction

\(f(5)=\frac{128}{20}=\frac{32}{5}\).

Answer:

B. \(\frac{32}{5}\)