Analyze graph transformations across radical, rational, exponential, logarithmic, and other functions; recognize even and odd functions.
Prove evenness using domain symmetry and f(-x)
Problem
Test \(f(x)~=~x^4~-~3x^2~+~1\) for evenness. Address domain symmetry, simplify \(f(-x)\), compare it with \(f(x)\), and state the conclusion.
Big Picture
What this problem is really about
An evenness proof has two gates: the domain must admit each input together with its opposite, and the outputs must satisfy the defining equality. Substitute negative x everywhere with parentheses intact, simplify each power before comparing, and let the resulting expression—not the graph’s appearance—determine whether the equality holds throughout the domain.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
