Evaluate the function at the given values of the independent variable and simplify.
f left parenthesis x right parenthesis equals StartFraction 7 x squared minus 1 Over x squared EndFraction
​(a) f left parenthesis 4 right parenthesis    ​(b) f left parenthesis negative 4 right parenthesis    ​(c) f left parenthesis negative x right parenthesis
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Part 1
​(a) f left parenthesis 4 right parenthesisequals

enter your response here ​(Type an integer or a fraction. Simplify your​ answer.)

For part (a), \( f(4) = 6.9375 \) or \( 6 \frac{15}{16} \).

Would you like more details or have any questions? Here are some follow-up queries to deepen your understanding:

1. How is the function behavior affected as \( x \) increases?
2. What happens to \( f(x) \) as \( x \to 0 \)?
3. How would you represent \( f(x) \) graphically?
4. How does \( f(x) \) change for negative values of \( x \)?
5. Can you identify any vertical asymptotes in the function?

**Tip:** When simplifying fractions, always try to check if both the numerator and the denominator share common factors.

Evaluate the function at the given values of the independent variable and simplify. f(x) = (7x^2 - 1) / x^2 (a) f(4) (b) f(-4) (c) f(-x)

Learn how to evaluate the rational function f(x) = (7x^2 - 1) / x^2 at different values such as f(4), f(-4), and f(-x). This problem covers algebraic concepts like rational functions and function evaluation, ideal for Grades 9-11 students.

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