MHB Find value of X in this equation

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To find the value of x in the equation f'g(x)=3/2, clarity is needed on the notation used. The discussion suggests that f' typically refers to the derivative of f, leading to the interpretation that f'g(x) means the derivative of f multiplied by g evaluated at x. There is confusion regarding whether it should be expressed as f'(x)g(x) or as a composition of functions. The assumption is made that the correct interpretation is f'(x)g(x), as other interpretations may lead to contradictions. Clear notation is essential for solving the equation effectively.
aruwin
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Hi, everyone.
Can someone guide me in finding the value of x in this equation?
I have left calculus for a very long time and I came across this question and wanted to try but I have forgotten a lot of things.
f(x)=5+2x and g(x)=2^x

Find the possible value of x such that f'g(x)=3/2
 
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aruwin said:
Find the possible value of x such that f'g(x)=3/2
It depends on what you denote by $f'g(x)$. Usually $f'$ denotes the derivative of $f$; in this case $f'g(x)$ means the derivative of $f$ multiplied by the value of $g$ at $x$. However, it is not clear at what value $f'$ is taken. If it said $f'(x)g(x)$, then there would be no questions.

The second option is that you mean the composition of $f$ and $g$, which is usually denoted by $(f\circ g)(x)$. Could you say what you mean?
 
f'(g(x)) = 3/2 is impossible, so I'm assuming it's f'(x) g(x).

-Dan
 

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