定理2.33(链式法则:光滑流形Chain Rule: smooth manifolds)。令 \Phi : {M}^{m} \rightarrow {N}^{n} 和 \Psi : {N}^{n} \rightarrow {P}^{k} 为光滑流形 M, N 和 P 之间的两个光滑映射(smooth manifolds),则有: $$ {\left( \Psi \circ \Phi \right) }_{ * } = {\Psi }_{ *...
rule n. 1.[C]规则,惯例 2.[U]统治,控制,支配 v.[T,I] 规定,统治 function n.[C] 1.官能,机能 2.功能,作用;用途;目的 3.职责;职务;职业 4.重大聚会,宴会;宗教仪式 5.【数】函数 6.应变量,随他物的变化而变化的事物 7.【计】功能 8. rule by rule adj. 依法理规则 inverse flame 倒焰...
Rule: Horizontal Line Test A function ff is one-to-one if and only if every horizontal line intersects the graph of ff no more than once. Figure 2. (a) The function f(x)=x2f(x)=x2 is not one-to-one because it fails the horizontal line test. (b) The function f(x)=x3f(x)...
into a function of y. We know that Tan2[x]=Sin2[x](Cos[x])2=y2 and Sin2[x]+(Cos[x])2=1, so we can express (Cos[x])2 in terms of y.The Inverse Function Rule can be used numerically even when the formula for the inverse function is not known. The next exercise shows ...
For, when the inverse is di?erentiable, we may apply this chain rule to di?erentiate the relation F ?1(F (x)) = x to obtain DF ?1(q0) DF (p0) = I , q0 = F (p0), 4 CHAPTER 4. INVERSE FUNCTION THEOREM where I is the identity map. We conclude that DF ?1(q0) = ...
➢f-1notatesaninversefunction.(not1/f)WHAT??Findtheinverseoff(x)=4x-2 x *4 -2 4x-2 (x+2)/4 /4 +2 x So f-1(x)=(x+2)/4 Thingstonote..➢Thedomainoff-1istherangeoff.➢Thegraphofaninversefunctioncanbe foundbyreflectingafunctionintheliney=x y=ex,y=xandy=lnx 5 4 y=ex...
Inverse Composition Rule Lesson Summary Frequently Asked Questions How do you know if a graph has an inverse function? The graph must be one-to-one and onto. This is verified by the graph of the function passing the vertical and horizontal line test or by looking at the equation. If ther...
Inverse function theoremLipschitz mapBanach spaceChain ruleWe establish the following converse of the well-known inverse function theorem. Let g : U → V and f : V → U be inverse homeomorphisms between open subsets of Banach spaces. If g is differentiable of class Cp and f if locally ...
Recapofinverseofafunction. Inversefunctionswithexandlnx Whatisit? INVERSEFUNCTION–reversingafunction,“undoing”. f-1notatesaninversefunction.(not1/f) WHAT?? Findtheinverseoff(x)=4x-2 x *4 4x-2 -2 (x+2)/4 x /4 +2 So f-1(x)=(x+2)/4 ...
inverse function- a function obtained by expressing the dependent variable of one function as the independent variable of another; f and g are inverse functions if f(x)=y and g(y)=x function,mapping,mathematical function,single-valued function,map- (mathematics) a mathematical relation such that...