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Mathematics 22 Online
OpenStudy (iwanttogotostanford):

Find x-y

OpenStudy (iwanttogotostanford):

someone please

OpenStudy (iwanttogotostanford):

@Erak

jimthompson5910 (jim_thompson5910):

can you post a screenshot or draw out the function?

OpenStudy (iwanttogotostanford):

sure

jimthompson5910 (jim_thompson5910):

thanks

OpenStudy (iwanttogotostanford):

no thank you!

jimthompson5910 (jim_thompson5910):

So one thing we could have is \[\Large f(x) = \frac{2}{x}+9\] \[\Large g(x) = x^2\]

OpenStudy (iwanttogotostanford):

so that would be the two separated?

OpenStudy (iwanttogotostanford):

and the first step?

jimthompson5910 (jim_thompson5910):

So one thing we could have is \[\Large f(x) = \frac{2}{x}+9\] \[\Large g(x) = x^2\] Notice what happens when we replace every copy of 'x' with g(x) \[\Large f(x) = \frac{2}{x}+9\] \[\Large f({\color{red}{x}}) = \frac{2}{{\color{red}{x}}}+9\] \[\Large f({\color{red}{g(x)}}) = \frac{2}{{\color{red}{g(x)}}}+9\] \[\Large f({\color{red}{g(x)}}) = \frac{2}{{\color{red}{x^2}}}+9\] So I replaced every 'x' with g(x). Then I replaced the g(x) on the right hand side with x^2

jimthompson5910 (jim_thompson5910):

So to sum things up If \[\Large f(x) = \frac{2}{x}+9\] \[\Large g(x) = x^2\] then \[\Large f(g(x)) = \frac{2}{x^2}+9\]

jimthompson5910 (jim_thompson5910):

yes @iwanttogotostanford

jimthompson5910 (jim_thompson5910):

they just want to know the functions f(x) and g(x)

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