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urp:algebra [2021-11-08] nerf_herder [Powers & Radicals] |
urp:algebra [2021-11-08] nerf_herder [Functions] |
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**quadratic formula**: x = (-b ±√(b²-4ac)) / 2a | **quadratic formula**: x = (-b ±√(b²-4ac)) / 2a | ||
+ | |||
+ | **PEMBAS/BODMAS ** - order of operations: Parentheses (brackets), exponents (order), multiply/divide, add/subtract | ||
==== System of equations==== | ==== System of equations==== | ||
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composition of functions: (f’g)(x) = f(g(x)), order of evaluation is important | composition of functions: (f’g)(x) = f(g(x)), order of evaluation is important | ||
- | inverse of function - only possible if no two values of x produce the same result | + | |
+ | **Inverse** of a function - only possible if no two values of x produce the same result | ||
+ | Example: To find f⁻¹(x) for f(x) = 5x + 3 | ||
+ | y = 5x + 3 | ||
+ | y-3 = 5x | ||
+ | x = (y-3)/5 | ||
+ | f⁻¹(x) = (x-3)/5 (replace y with x on the last step, | ||
+ | since x is input to the function, and y is output) | ||
graphing an inverse: reflection of the graph about the line y=x | graphing an inverse: reflection of the graph about the line y=x | ||