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\(\text{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.}\)

 Jul 18, 2019
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If  f(x)  is defined on  [ -8, 4].....this implies that  the function is defined for f(-8) to f(4) inclusive

 

So

 

g(x)  = f(-2x) = f(-8)   implies that   -2x = - 8  ⇒  x  = 4

 

And

 

g(x)  =  f(-2x)  = f(4)  implies that  -2x  = 4  ⇒  x = -2

 

So....the domain for g  is  [ -2, 4 ]

 

 

cool cool cool

 Jul 18, 2019

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