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

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

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.**