We are given the functions f and g with the rules:
![\displaystyle{ f(x)= \frac{x-9}{x+5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20f%28x%29%3D%20%5Cfrac%7Bx-9%7D%7Bx%2B5%7D%20)
and
![\displaystyle{ g(x)= \frac{-5x-9}{x-1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20g%28x%29%3D%20%5Cfrac%7B-5x-9%7D%7Bx-1%7D%20)
.
First, we prove that f(g(x))=x:
![\displaystyle{ f(g(x))= \frac{g(x)-9}{g(x)+5}=\frac{\frac{-5x-9}{x-1}-9}{\frac{-5x-9}{x-1}+5}=\frac{\frac{-5x-9}{x-1}-9\cdot\frac{x-1}{x-1}}{\frac{-5x-9}{x-1}+5\cdot\frac{x-1}{x-1}}\\\\](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20f%28g%28x%29%29%3D%20%5Cfrac%7Bg%28x%29-9%7D%7Bg%28x%29%2B5%7D%3D%5Cfrac%7B%5Cfrac%7B-5x-9%7D%7Bx-1%7D-9%7D%7B%5Cfrac%7B-5x-9%7D%7Bx-1%7D%2B5%7D%3D%5Cfrac%7B%5Cfrac%7B-5x-9%7D%7Bx-1%7D-9%5Ccdot%5Cfrac%7Bx-1%7D%7Bx-1%7D%7D%7B%5Cfrac%7B-5x-9%7D%7Bx-1%7D%2B5%5Ccdot%5Cfrac%7Bx-1%7D%7Bx-1%7D%7D%5C%5C%5C%5C%20)
![=\displaystyle { \frac{ \frac{-5x-9-9x+9}{x-1} }{\frac{-5x-9+5x-5}{x-1}}= \frac{-5x-9-9x+9}{-5x-9+5x-5} = \frac{-14x}{-14}=x.](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%20%7B%20%20%5Cfrac%7B%20%5Cfrac%7B-5x-9-9x%2B9%7D%7Bx-1%7D%20%7D%7B%5Cfrac%7B-5x-9%2B5x-5%7D%7Bx-1%7D%7D%3D%20%5Cfrac%7B-5x-9-9x%2B9%7D%7B-5x-9%2B5x-5%7D%20%3D%20%5Cfrac%7B-14x%7D%7B-14%7D%3Dx.%20)
Similarly, we prove that g(f(x))=x:
![\displaystyle{ g(f(x))= \frac{-5f(x)-9}{f(x)-1}= \frac{-5\cdot \frac{x-9}{x+5}-9\cdot \frac{x+5}{x+5}}{\frac{x-9}{x+5}-\frac{x+5}{x+5}}= \frac{-5(x-9)-9(x+5)}{x-9-(x+5)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20g%28f%28x%29%29%3D%20%5Cfrac%7B-5f%28x%29-9%7D%7Bf%28x%29-1%7D%3D%20%5Cfrac%7B-5%5Ccdot%20%5Cfrac%7Bx-9%7D%7Bx%2B5%7D-9%5Ccdot%20%5Cfrac%7Bx%2B5%7D%7Bx%2B5%7D%7D%7B%5Cfrac%7Bx-9%7D%7Bx%2B5%7D-%5Cfrac%7Bx%2B5%7D%7Bx%2B5%7D%7D%3D%20%5Cfrac%7B-5%28x-9%29-9%28x%2B5%29%7D%7Bx-9-%28x%2B5%29%7D%20)
By using cross multiplication x= 3×7÷5=4.2
the answer is 4.2
Answer:
17 - 7m
Step-by-step explanation:
Assuming you require to subtract the expressions, then
16 + m - (8m - 1) ← distribute parenthesis by - 1
= 16 + m - 8m + 1 ← collect like terms
= 17 - 7m
Answer:
$900
Step-by-step explanation:
If she holds $500 and she is charged 15%; it means
The interest she pays per month is ;
$500 × 15/100 = $75
Then annually meaning for 12 months, she pays;
$75 × 12 = $900
Yes it can. Just have too figure out why then you will be good