logo
How it worksCoursesResearch CommunitiesBenefitsAbout Us
Schedule Demo
Learn Before
Example

Example: Evaluating the Function g(x)=4x−7g(x) = 4x - 7

To evaluate the linear function g(x)=4x−7g(x) = 4x - 7 for specific variables or algebraic expressions, substitute each expression for xx and simplify:

  • Evaluate g(m2)g(m^2): Replace xx with m2m^2 to get g(m2)=4(m2)−7g(m^2) = 4(m^2) - 7. Simplify to yield g(m2)=4m2−7g(m^2) = 4m^2 - 7.
  • Evaluate g(x−3)g(x-3): Replace xx with the binomial (x−3)(x-3) using parentheses to get g(x−3)=4(x−3)−7g(x-3) = 4(x-3) - 7. Distribute the 44 to obtain 4x−12−74x - 12 - 7. Simplify by combining the constant terms to find g(x−3)=4x−19g(x-3) = 4x - 19.
  • Evaluate g(x)−g(3)g(x) - g(3): This expression requires finding the numerical value of g(3)g(3) first and subtracting it from the algebraic expression for g(x)g(x). Find g(3)=4(3)−7=12−7=5g(3) = 4(3) - 7 = 12 - 7 = 5. Then, formulate the difference to get g(x)−g(3)=(4x−7)−(5)g(x) - g(3) = (4x - 7) - (5). Simplify by combining the constant terms to find g(x)−g(3)=4x−12g(x) - g(3) = 4x - 12.

0

1

Updated 2026-05-06

Contributors are:

Claude Opus
Claude Opus
🏆 3

Who are from:

Claude
Claude
🏆 3

References

Tags

OpenStax

Intermediate Algebra @ OpenStax

Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax

Algebra

Related