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Video: Dab tsi yog inverse function hauv calculus?
2024 Tus sau: Miles Stephen | [email protected]. Kawg hloov kho: 2023-12-15 23:36
Hauv lej, ib inverse muaj nuj nqi (los yog anti- muaj nuj nqi ) yog a muaj nuj nqi uas "reverses" lwm muaj nuj nqi :if cov muaj nuj nqi f siv rau qhov kev nkag x muab qhov tshwm sim ntawm y, tom qab ntawd siv nws inverse muaj nuj nqi g rau y muab qhov tshwm sim x, thiab vice versa, i.e., f(x) = y yog thiab tsuas yog g(y) = x.
Yog li ntawd, yuav ua li cas koj pom qhov inverse ntawm ib tug muaj nuj nqi nyob rau hauv calculus?
Nrhiav qhov Inverse ntawm Kev Ua Haujlwm
- Ua ntej, hloov f(x) nrog y.
- Hloov txhua x nrog y thiab hloov txhua y nrog x.
- Kho qhov sib npaug ntawm Kauj Ruam 2 rau y.
- Hloov y nrog f − 1 (x) f − 1 (x).
- Txheeb xyuas koj txoj haujlwm los ntawm kev txheeb xyuas tias (f∘f−1)(x) = x (f ∘ f − 1) (x) = x and (f−1∘f)(x) = x (f − 1 ∘ f) (x) = x yog ob qho tseeb.
piv txwv inverse function yog dab tsi? Inverse functions , nyob rau hauv qhov kev txiav txim siab tshaj plaws, yog muaj nuj nqi uas "rov qab" ib leeg. Rau piv txwv , yog tias f siv a rau b, ces tus thim rov qab , f − 1 f^{-1} f−1f, start superscript, minus, 1, end superscript, yuav tsum coj b mus rau a.
Ntawm no, koj ua li cas sib txawv inverse functions?
Derivatives ntawm Inverse Trigonometric Functions
- Siv lub inverse function theorem los nrhiav qhov derivative ntawm g(x)=sin−1x.
- Txij li rau x hauv lub caij nyoog [−π2, π2], f (x) = sinx yog inverse of g(x) = sin − 1x, pib los ntawm kev nrhiav f′(x).
- f′(x) = cosx.
- f′(g(x))=cos(sin−1x)=√1−x2.
- g′(x)=ddx(sin−1x)=1f′(g(x))=1√1−x2.
Self inverse function yog dab tsi?
A tus kheej inverse muaj nuj nqi yog a muaj nuj nqi f, xws li y = f(x), nrog rau cov khoom tshwj xeeb uas ff(x) = x, lossis sau lwm txoj kev, f(x) = f − 1(x)
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