there are many combinations for it, but we can settle for say
![\bf \begin{cases} f(x)=x+2\\[1em] g(x)=\cfrac{9}{x^2}\\[-0.5em] \hrulefill\\ (f\circ g)(x)\implies f(~~g(x)~~) \end{cases}\qquad \qquad f(~~g(x)~~)=[g(x)]+2 \\\\\\ f(~~g(x)~~)=\left[ \cfrac{9}{x^2} \right]+2\implies f(~~g(x)~~)=\cfrac{9}{x^2}+2](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20f%28x%29%3Dx%2B2%5C%5C%5B1em%5D%20g%28x%29%3D%5Ccfrac%7B9%7D%7Bx%5E2%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20%28f%5Ccirc%20g%29%28x%29%5Cimplies%20f%28~~g%28x%29~~%29%20%5Cend%7Bcases%7D%5Cqquad%20%5Cqquad%20f%28~~g%28x%29~~%29%3D%5Bg%28x%29%5D%2B2%20%5C%5C%5C%5C%5C%5C%20f%28~~g%28x%29~~%29%3D%5Cleft%5B%20%5Ccfrac%7B9%7D%7Bx%5E2%7D%20%5Cright%5D%2B2%5Cimplies%20f%28~~g%28x%29~~%29%3D%5Ccfrac%7B9%7D%7Bx%5E2%7D%2B2)
Answer:
Choice 3 is your answer
Step-by-step explanation:
The format of the function when you move it side to side or up and down is
f(x) = (x - h) + k,
where h is the side to side movement and k is up or down. The k is easy, since it will be positive if we move the function up and negative if we move the function down from its original position.
The h is a little more difficult, but just remember the standard form of the side to side movement is always (x - h). If our function has moved 3 units to the left, we fit that movement into our standard form as (x - (-3)), which of course is the same as (x + 3). Our function has moved up 5 units, so the final translation is
g(x) = f(x + 3) + 5, choice 3 from the top.
Vertical shift is -2. Horizontal shift is 1. Check the box that says reflect over x-axis. Horizontal shrink should be 4. Then to check if it looks right go to Desmos.com and in the graphing calculator put in y=-4(x-1)^2-2 and see if it looks like the one you did in your work
8z=4(2z+1)
First you would distribute the constant into the numbers in the parentheses. so
8z=8z+4
then you would combine like terms which in this case would result in a zero.
8z-8z=0 So the z would be zero or no solution.
Hi
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