Can you do 1b please, thanks 1. (a) Use \(\sqrt{x} - \sqrt{y} = \frac{x-y}{\sqrt{x}+\sqrt{y}}\) to show that \( f : [0, \infty) \rightarrow \mathbb{R} \) with \( f(x) = \sqrt{x} \) is continuous \( x_0 \in (0, \infty) \). Proceed as follows. As \( x_0 \neq 0 \), there exists some positive number \( a \) such that \( x_0 \in (a, \infty) \). Choose \( \delta \) small enough so that \( x \) will lie in \( (a, \infty) \) as well. Separately, show that \( f \) is continuous at \( x_0 = 0 \).(b) (Continuity and composition). Suppose \( f : D \rightarrow \mathbb{R} \) and \( g : E \rightarrow \mathbb{R} \) with \( \text{im} \, f \subseteq E \). Assume that \( f \) is continuous at \( x_0 \in D \) and \( g \) is continuous at \( f(x_0) \in E \). Then the composition \( g \circ f : D \rightarrow \mathbb{R} \) is continuous at \( x_0 \).

(b) (Continuity and composition) Suppose and with .Assume that is continuous at and is continuous at .Then the composition is continuous at .Given that and are functions with .Given that is continuous at , that means for , there exists such that whenever .Also, is continuous at , that means for , there exists such that whenever i.e., whenever .Thus, .So, is continuous at .Hence, the function is continuous at .