Suppose a function f(x) has a domain of (-inf,inf) and range [-11,3]. If we define a new function g(x) by g(x)=f(6x) +1, then what is the range of g(x)? Express your answer in interval notation. Thank you!

Answer 1

Since the domain of f is all x, the range of f(6x) is the same as the range of f(x). The graph is just contracted horizontally by a factor of 6. The range is unaffected.

So, the range of g(x) = f(6x)+1 is just [-11,3]+1 = [-10,4]

Things would have been stickier had the domain been restricted. Then we might not know whether g(x) was even defined for all the values in the domain of f(x).

Answer 2

Suppose a function f(x) is defined on the domain [-8,4]. If we define a new function g(x) by g(x) = f(-2x), then what is the domain of g(x)? Express your answer in interval notation.