Sum, composition and inverse of functions
Add two functions, keep the order in a composite function, find the inverse of a machine by undoing its steps, build the inverse graph by reflecting in y = x, and use a horizontal line to see which functions have an inverse.
- سوريا: الصف ١١
- فلسطين: الصف ٩
- إيران: الصف ١١
- أفغانستان: الصف ١٠
- أوكرانيا: الصف ١١
- روسيا: الصف ١٠
- ألمانيا: الصف ١٠
- بريطانيا: السنة ١٠
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
(f + g)(x) means f(x) + g(x): add the values of the two functions at the same x. Products and quotients work the same way; for a quotient g(x) must not be zero.
In (g∘f)(x) = g(f(x)) f is done first and then g. The order matters: the machine "× 2, then + 1" is not "+ 1, then × 2".
To find an التابع العكسي undo the steps in reverse order. The graph of f−١ is the reflection of the graph of f in the line y = x: the point (a, b) goes to (b, a). Only a function that gives each output once (تابع متباين, the horizontal-line test) has an inverse.