# Part - 2 Lecture - 6 Chapter 1 Relations and Functions

Don’t stop when you’re tired. STOP when you are DONE. – **Unknown**

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Lecture 6 Part 2 Questions from Exercise 1.3, NCERT Exemplar, Board’s Question Bank

Important details about inverse functions (Invertible Functions)

**3.** Let f : X → Y be an invertible function. Show that f has unique inverse. (N)

**4.** Let f : N → Y be a function defined as f (x) = 4x + 3, where, Y = {y ∈ N: y = 4x + 3 for some x ∈ N}. Show that f is invertible. Find the inverse. (N)

**5.** Let \( Y= \{n^2: n \in N\} \subset N\). Consider \(f:N \rightarrow Y \) as \(f(n)=n^2\). Show that f is invertible. Find the inverse of f. (N)

**6.** If \(f(x)=\frac{4x+3}{6x-4},x \ne \frac{2}{3}\), show that \(fof(x)=x\), for all \( x\ne \frac{2}{3}\). What is the inverse of f ? (N) (Involution or Involutory Function)

**7.** Show that f:[-1,1]→R, given by \(f(x)=\frac{x}{x+2}\) is one-one. Find the inverse of the function f:[-1,1]→Range f. (N)

**8.** Let \(f: R-\left \{ -\frac{4}{3}\right \} \rightarrow R\) be a function defined as \(f(x)=\frac{4x}{3x+4}\). The inverse of f is the map \( g:\text{Range}f \rightarrow R -\left \{-\frac{4}{3}\right \}\) given by (N)* a.* \(g(y)=\frac{3y}{3-4y} \)

*\(g(y)=\frac{4y}{4-3y} \)*

**b.***\( g(y)=\frac{4y}{3-4y}\)*

**c.***\(g(y)=\frac{3y}{4-3y} \)*

**d.**