Part - 2 Lecture - 6 Chapter 1 Relations and Functions

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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. $$g(y)=\frac{3y}{3-4y}$$
b. $$g(y)=\frac{4y}{4-3y}$$
c.$$g(y)=\frac{4y}{3-4y}$$
d. $$g(y)=\frac{3y}{4-3y}$$