1 Miscellaneous Section b is the question Consider a continu

1: Miscellaneous:

Section (b) is the question

Consider a continuous function, f: R rightarrow R. Using the definition of continuity, show that the function g(x) = f(3x) is also continuous. (c) Consider the function

Solution

f : R to R is continuous

That is f is continuous at every point of R

let x belongs to R then f is continuous at x

f is continuous at x for every x in R

x in R so 3x is also in R

Since f is continuous at every point of R

f is continuous at 3x,for every x in R

Hence g(x)=f(3x) is continuous