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Dab tsi yog inverse function hauv calculus?
Dab tsi yog inverse function hauv calculus?

Video: Dab tsi yog inverse function hauv calculus?

Video: Dab tsi yog inverse function hauv calculus?
Video: Dag Kuv Dab Tsis 2024, Kaum ib hlis
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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

  1. Ua ntej, hloov f(x) nrog y.
  2. Hloov txhua x nrog y thiab hloov txhua y nrog x.
  3. Kho qhov sib npaug ntawm Kauj Ruam 2 rau y.
  4. Hloov y nrog f − 1 (x) f − 1 (x).
  5. 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

  1. Siv lub inverse function theorem los nrhiav qhov derivative ntawm g(x)=sin−1x.
  2. 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).
  3. f′(x) = cosx.
  4. f′(g(x))=cos(sin−1x)=√1−x2.
  5. 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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