Asked by Trish Goal

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!

Answers

Answered by Steve
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).
Answered by Sexata Mendez
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.
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