In Mathematics AA HL, students are expected to solve inequalities of the form g(x) ≥ f(x), where g(x) and f(x) are functions. This type of inequality compares two functions and asks for the values of x where one function is greater than or equal to the other.
One method to solve g(x) ≥ f(x) is by graphing both functions and identifying the regions where g(x) is above or on f(x).
Consider the inequality $x^2 + 1 \geq 2x$. To solve this graphically:
The solution is all real numbers, since $x^2 + 1 \geq 2x$ simplifies to $(x-1)^2 \geq 0$.
When graphing, pay attention to the points of intersection between g(x) and f(x). These points often represent the boundaries of the solution set.
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