Let $f: \mathrm{X} \rightarrow \mathrm{Y}$ be an invertible function. Show that $f$ has unique inverse. (Hint: suppose $g_{1}$ and $g_{2}$ are two inverses of $f .$ Then for all $y \in Y$, $f \circ g_{1}(y)=1_{Y}(y)=f \circ g_{2}(y) .$ Use one-one ness of $\left.f\right)$

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Algebra

NCERT Class 12 Part 1 - Math

Chapter 1

Relations and Functions

Section 3

Types of Functions

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Video Transcript

in this problem of relation and function we have to assume that defense and F is from X to Y. So this is from extra way X two white be convertible funds and that means this is 11 and on to function. And now we have to show that this function has unique universe. So function is convertible. So we see that difference is in vertebral convertible. That means this has unique universe. So now we have to let suppose it has two universes. So suppose G one and G two. So this is what is the G two, jeevan and G two. R two universe. Suppose there is no unique universe when N G two. R two inverse of function of funds. And F in that case in that case this would be from this year we say that here F of G Y. So this would be F of G Y. So this would be F G and Y. Actually, so the G U N Y is equals two. Here this should be equal to wife and F of and F of G two Y is equal to white. So from here we conclude that F of G u n Y should be equal to F of G two white. From here, we can write it F of G Y. So this would be F of G and Y, and that's what we have up here, F F G two white. And now this concern is said to be equal if G and Y is equal to G two Y. That means here we have. Why? Why? That means G and G equals two G two. So hence we say that the pension age has hence the function F health, unique, unique in words. So this is the answer.

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