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anonymous
 one year ago
PLEASE HELP!!! I HAVE NO IDEA WHAT IM DOING
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = quantity x8/ x+7. and gx) = 7x  8/x1.
anonymous
 one year ago
PLEASE HELP!!! I HAVE NO IDEA WHAT IM DOING Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = quantity x8/ x+7. and gx) = 7x  8/x1.

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3I don't understand what the functions are. Can you use parentheses to show the numerator and denominator?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0agree I can't figure it out either. Can you draw the functions?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Is this f(x)? \(f(x) = \dfrac{x  8}{x + 7} \) Is g(x) \(g(x) = \dfrac{7x  8}{x  1} \) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yesss @mathstudent55

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Ok. Now we can start. Before we start, next time do it this way. Then there won't be any confusion: f(x) = (x  8)/(x+7) g(x) = (7x  8)/(x  1) Also, you can draw the functions or use the Latex editor.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Ok. Let's do it. Functions f(x) and g(x) are inverses if f(g(x)) = g(f(x)) = x

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3\(f(x) = \dfrac{x  8}{x + 7}\) f(g(x)) means to evaluate f(x) using g(x) \(g(x) = \dfrac{7x  8}{x  1} \), so we replace x of f(x) with \(\dfrac{7x  8}{x  1}\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3\(\large f(x) = \dfrac{x  8}{x + 7} \) \(\large f(g(x)) = f\left(\dfrac{7x  8}{x  1}\right)\) \(\large f(g(x))\Large = \dfrac{\frac{7x  8}{x  1}  8}{\frac{7x  8}{x  1} + 7}\) You see, where there was an x in the f(x) function, we now have what g(x) is equal to.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Now we need to simplify that fraction.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3\(\large f(g(x))\Large = \dfrac{\left( \frac{7x  8}{x  1}  8 \right)(x  1)}{\left( \frac{7x  8}{x  1} + 7 \right) (x  1)}\) \(\large f(g(x))\Large = \dfrac{7x  8  8(x  1)}{7x  8 + 7 (x  1)}\) \(\large f(g(x))\Large = \dfrac{7x  8  8x + 8}{7x  8 + 7x  7}\) \(\large f(g(x))\Large = \dfrac{15x}{15}\) \(\large f(g(x))\Large = x\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3That shows that f(g(x)) = x. Now we need to show that g(f(x)) = x

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3\(\large g(x) = \dfrac{7x  8}{x  1} \) \(\large f(x) = \dfrac{x  8}{x + 7} \) Now we replace the x on the right side of the g(x) function with what f(x) is equal to, \(\dfrac{x  8}{x + 7} \) \(\large g(f(x)) \Large = \dfrac{7 \left( \frac{x  8}{x + 7} \right) 8}{ \frac{x  8}{x + 7}  1}\) \(\large g(f(x))\Large = \dfrac{\left[ 7 \left( \frac{x  8}{x + 7} \right) 8 \right](x + 7)}{\left[ \frac{x  8}{x + 7}  1 \right](x + 7)} \) \(\large g(f(x))\Large = \dfrac{7 (x  8) 8 (x + 7)}{x  8  (x + 7)} \) \(\large g(f(x))\Large = \dfrac{7x + 56 8x  56)}{x  8  x  7} \) \(\large g(f(x))\Large = \dfrac{15x}{ 15 } \) \(\large g(f(x))\Large = x\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3Now we have also shown that g(f(x)) = x. Since we now know that f(g(x)) = g(f(x)) = x, we have confirmed that the functions f(x) and g(x) are inverses of each other.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you sooooooo much @mathstudent55

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.3You are very welcome.
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