Answer
q1.
Given: ![y = \frac{9}{x^2}+2](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B9%7D%7Bx%5E2%7D%2B2)
Rewrite this function in the way as;
![y = \frac{9}{g(x)} + 2](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B9%7D%7Bg%28x%29%7D%20%2B%202)
then;
and ![f(x) = \frac{9}{x} + 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B9%7D%7Bx%7D%20%2B%202)
q2.
Given the function:
and ![g(x) = \frac{x-3}{9}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7Bx-3%7D%7B9%7D)
Confirm f and g are inverses by showing f(g(x)) =x and g(f(x)) =x
First show f(g(x)) =x
f(g(x)) = 9(g(x)) + 3
Substitute the function g(x) we have;
![f(g(x)) = 9(\frac{x-3}{9}) + 3](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%209%28%5Cfrac%7Bx-3%7D%7B9%7D%29%20%2B%203)
or
= x -3 + 3 = x
f(g(x)) =x
Similarly show that: g(f(x)) =x
![g(f(x)) = \frac{f(x)-3}{9}](https://tex.z-dn.net/?f=g%28f%28x%29%29%20%3D%20%5Cfrac%7Bf%28x%29-3%7D%7B9%7D)
Substitute the value of function g(x) we have;
![g(f(x)) =\frac{9x+3-3}{9}](https://tex.z-dn.net/?f=g%28f%28x%29%29%20%3D%5Cfrac%7B9x%2B3-3%7D%7B9%7D)
Simplify:
![g(f(x)) =\frac{9x}{9}](https://tex.z-dn.net/?f=g%28f%28x%29%29%20%3D%5Cfrac%7B9x%7D%7B9%7D)
hence proved!
Therefore, f and g are inverse of each other after showing f(g(x)) =x and g(f(x)) =x
Answer:
The mean number of scores per game is 8
Step-by-step explanation:
Since we know we can find the mean by adding all the numbers and dividing them by many numbers there were. Once you add 8, 14, 4, 7, 6, 4, and 7, you will get 64. Since there were 8 numbers, you divide 64 by 8 to get 8.
You can write it in point-slope form like I did at the top, but I simplified it to slope-intercept (the answer with a square around it)
Find the solution set of x: x^2-7x= - 10.
Answer:
(x − 2)(x −5)
Step-by-step explanation:
x² - 7x = - 10
x² - 7x + 10 = 0
Find two numbers that when added together make −7 , and when multiplied make - 10.
The numbers − 2 and −5 fit the criteria.
x2− 7x + 10 = (x − 2)(x −5)
Answer:
It comes down to what the equals sign means. It means, that the two things mentioned on either side of the equation are the same thing. If you do something to the left side, you have presumably changed it.
Step-by-step explanation:
Hope this helps, If it did, then I would really appreciate it if you gave me Brainliest, I only need one more to rank up and it has taken forever to get to where I am currently. Thanks.