Handwritten Notes on Inverse Functions | MATH 1315, Study notes of Mathematics

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Lectwe |0 — Seckion 245 — Tnverse Sunckions One-to-one Funekions R set of ordered paivs 15 called a velation . A velation in which each Fivst element 1S paired with a anigue Seco nd clement 1S called 4 Cunckion, i Function \n which each Second clement 15 paired with a wnigae Sivgt element 15 called a one-to-one Function , Trvevse of « one-to-one furckion The inverse of & one-tp-one Function [5 obbained by reversing the. ovdeved ‘paivs. The inverse ok a one-to-one Cunctinn 1% also a one-to-one function. Notation for the iavevse of function F is $7! Ex. Suppose f= (45), (5,0)§. Is ¢ invertible ® TF 50, Grad FF, Yes, it's invertible Cinverbible means ave-to-one) Fr\s 16,9, (.5)§ Rules (FY t= $F (the insene of the inverse 1 the ouigival Funckion)) Ex. Suppose F=3U,2),(5,2),(6,7)8. Find F, Since. $ i not a one-to-one function, itdoesrtf have a functional inverse.