Math Problem Statement

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 Question content area bottom Part 1 ​(a) f left parenthesis 4 right parenthesisequals

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

Solution

For part (a), f(4)=6.9375f(4) = 6.9375 or 615166 \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 xx increases?
  2. What happens to f(x)f(x) as x→0x \to 0?
  3. How would you represent f(x)f(x) graphically?
  4. How does f(x)f(x) change for negative values of xx?
  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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Rational Functions
Function Evaluation

Formulas

f(x) = (7x^2 - 1) / x^2

Theorems

Symmetry of Even and Odd Functions
Simplification of Rational Expressions

Suitable Grade Level

Grades 9-11

Related Recommendation

Rational Function Evaluation and Limits for f(x) = 1 / (7 - (1 / x) + 7x)

Evaluating Rational Function with Discontinuity: f(x) = x(x-2)/(x-1)

Evaluate the Rational Function f(x) = (x - 1) / (2x + 1) for x = 77

Evaluate f(-4) + f(2) and f(-4) - f(2) for Quadratic Function f(x) = x^2 + x - 7

Plotting Rational Functions: Asymptotes and X-Intercepts for f(x) = (7x)/(x-4)