Evaluate the function at the given values of the independent variable and simplify. \( f(x)=\frac{5 x^{2}-1}{x^{2}} \) \( \begin{array}{lll}\text { (a) } f(5) & \text { (b) } f(-5) & \text { (c) } f(-x) \\ \text { (a) } f(5)=\square & \text { (Type an integer or a fraction. Simplify your answer.) }\end{array} \)

To evaluate the function \( f(x) = \frac{5x^{2} - 1}{x^{2}} \) at the given values: (a) For \( f(5) \): \[ f(5) = \frac{5(5)^{2} - 1}{(5)^{2}} = \frac{5(25) - 1}{25} = \frac{125 - 1}{25} = \frac{124}{25} \] So, \( f(5) = \frac{124}{25} \). (b) For \( f(-5) \): \[ f(-5) = \frac{5(-5)^{2} - 1}{(-5)^{2}} = \frac{5(25) - 1}{25} = \frac{125 - 1}{25} = \frac{124}{25} \] So, \( f(-5) = \frac{124}{25} \). (c) For \( f(-x) \): \[ f(-x) = \frac{5(-x)^{2} - 1}{(-x)^{2}} = \frac{5x^{2} - 1}{x^{2}} = f(x) \] Therefore, \( f(-x) = f(x) \). Final results: - (a) \( f(5) = \frac{124}{25} \) - (b) \( f(-5) = \frac{124}{25} \) - (c) \( f(-x) = f(x) \)