Use the function gx f2x a What is the domain of g Write in

Use the function g(x) = f(2x) a) What is the domain of g? Write in interval notation. b) What is the range of g? Write in interval notation. c) Sketch the graph of g

Solution

(a). Unless the function f(x) is described, it is not possible to determine the domain of g(x) = f(2x). For example, if f(x) =x, then the domain of both f(x) and g(x) is (- ,). However, if f(x) =(x²-1)^1/2, then the domain of f(x) is (-, -1] and the domain of g(x) = f(2x) is (-, -1/2].

(b) If the range of the function f(x) is (a,b), where a and b are arbitrary real numbers, then the range of of g(x) = f(2x) is also (a,b), i.e. the range of f(x).

(c ). The graph of g(x) =f(2x) is the graph of f(x) scaled in the X- direction by a factor of ½. The new graph is obtained by compressing the old one horizontally by a factor of 2. Till f(x) is known, the graph of g(x) cannot be sketched.