Why your math homework might be missing a crucial step
In short: Many students assume that if two functions look like opposites, they must be inverses. This video demonstrates why checking the composition of functions is the only way to prove it.
The tutorial uses the specific functions f(x) = 2x - 3 and g(x) = ½x + 3 to show a common pitfall in high school algebra. While these functions appear to perform opposite operations, their compositions—f(g(x)) and g(f(x))—do not simplify back to x.
By showing that the results are not equal to x, the video clarifies that simple visual symmetry isn't enough for verification. It reinforces the rigorous algebraic requirement that an inverse must perfectly undo every operation of the original function.
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Sources
- Summary by Intellect · source: Verifying inverse functions by composition: not inverse | High School Math | Khan Academy
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