#### Questions Discussed:

**Question 1.** Let f :\{1, 3, 4\} \rightarrow \{1, 2, 5\} \text{ and } g:\{1, 2, 5\} \rightarrow \{1, 3\} be given by f = \{(1, 2), (3, 5), (4, 1)\} \text{ and } g = \{(1, 3), (2, 3), (5, 1)\} Write down gof. (N)

**Question 2.** If f = \{(5, 2), (6, 3)\}, g = \{(2, 5), (3, 6)\}, write f o g. (E)

**Question 3.** If the mappings f and g are given by f = \{(1, 2), (3, 5), (4, 1)\} \text{ and } g = \{(2, 3), (5, 1), (1, 3)\}, write f o g. (E)

**Question 4.** If f : \{1, 3\} \rightarrow \{1, 2, 5\} \text{ and } g: \{1, 2, 5\} \rightarrow \{1, 2, 3, 4\} be given by f = \{(1, 2), (3, 5)\}, g = \{( 1, 3), (2, 3), (5, 1 )\} , write gof . (B)

**Question 5.** Consider f : \mathbf{N} \rightarrow \mathbf{N}, g: \mathbf{N} \rightarrow \mathbf{N} \text{ and } h: \mathbf{N} \rightarrow \mathbf{R} defined as f (x) = 2x, g(y) = 3y + 4 \text{ and } h(z) = \sin z, \forall x, y \text{ and } z \text{ in } \mathbf{N}. Show that ho(gof) = (hog)of. (N)

**Question 6.** Find gof and fog, if (N)

**a.** f(x)=\,\,|x|\,\,\text{and }g(x)=\,\,|5x-2|

**b.** f(x)=8{{x}^{3}}\text{ and }g(x)={\displaystyle {{x}^{{\frac{1}{3}}}}}