Answer:
x=28
Step-by-step explanation:
Answer:
The inverse of g(x) is ![g^{-1}(x)=\frac{2x}{1-x}](https://tex.z-dn.net/?f=g%5E%7B-1%7D%28x%29%3D%5Cfrac%7B2x%7D%7B1-x%7D)
The domain of g(x) is (-∞,-2)U(-2,∞)
The domain of f(x) is (-∞,-1)U(-1,1)U(1,∞)
Step-by-step explanation:
Find the inverse of g(x).
![y=\frac{x}{x+2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bx%7D%7Bx%2B2%7D)
Solve for x
![x=y(x+2)](https://tex.z-dn.net/?f=x%3Dy%28x%2B2%29)
![x=xy+2y](https://tex.z-dn.net/?f=x%3Dxy%2B2y)
![x(1-y)=2y](https://tex.z-dn.net/?f=x%281-y%29%3D2y)
![x=\frac{2y}{1-y}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2y%7D%7B1-y%7D)
![g^{-1}(x)=\frac{2x}{1-x}](https://tex.z-dn.net/?f=g%5E%7B-1%7D%28x%29%3D%5Cfrac%7B2x%7D%7B1-x%7D)
Find the domain of g(x)
![g(x)=\frac{x}{x+2}](https://tex.z-dn.net/?f=g%28x%29%3D%5Cfrac%7Bx%7D%7Bx%2B2%7D)
Numerator and denominator have domain
(-∞,∞).
However, g(x) is undefined if the denominator is 0. Hence, x=-2 must be taken out of the domain. So, the domain of g(x) is
(-∞,-2)U(-2,∞).
Find the domain of f(x)
![f(x)=\frac{1}{x^{2} -1}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7Bx%5E%7B2%7D%20-1%7D)
The numerator and denominator have the domain
(-∞,∞)
However, f(x) is undefined if the denominator is 0. This rules out +1 and -1. So, the domain of f(x) is
(-∞,-1)U(-1,1)U(1,∞)
I am not sure what you mean for (ii).
Answer:
6a- 18
Step-by-step explanation:
![6(a-3) = 6a - 6(3) = 6a - 18](https://tex.z-dn.net/?f=6%28a-3%29%20%3D%206a%20-%206%283%29%20%3D%206a%20-%2018)
Since we have that the slope is m = 7/9 and the y-intercept is b = 12, we can write the equation of the line in slope-intercept form:
![\begin{gathered} y=mx+b \\ \Rightarrow y=\frac{7}{9}x+12 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3Dmx%2Bb%20%5C%5C%20%5CRightarrow%20y%3D%5Cfrac%7B7%7D%7B9%7Dx%2B12%20%5Cend%7Bgathered%7D)
to find three coordinate points, we can use arbitrary values on x to get the y-coordinate. To make things easier, let's use x = 9, 18 and 27:
![\begin{gathered} x=9 \\ \Rightarrow y=\frac{7}{9}(9)+12=7+12=19 \\ x=18 \\ \Rightarrow y=\frac{7}{9}(18)+12=7(2)+12=14+12=26 \\ x=27 \\ \Rightarrow y=\frac{7}{9}(27)+12=7(3)+12=21+12=33 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D9%20%5C%5C%20%5CRightarrow%20y%3D%5Cfrac%7B7%7D%7B9%7D%289%29%2B12%3D7%2B12%3D19%20%5C%5C%20x%3D18%20%5C%5C%20%5CRightarrow%20y%3D%5Cfrac%7B7%7D%7B9%7D%2818%29%2B12%3D7%282%29%2B12%3D14%2B12%3D26%20%5C%5C%20x%3D27%20%5C%5C%20%5CRightarrow%20y%3D%5Cfrac%7B7%7D%7B9%7D%2827%29%2B12%3D7%283%29%2B12%3D21%2B12%3D33%20%5Cend%7Bgathered%7D)
therefore, the line with slope m = 7/9 and y-intercept 12 passes through the three points (9,19), (18,26) and (27,33)
Answer:
6.4
Step-by-step explanation:
Add 3 + 1.45 + 1.2 + 0.75 = 6.4 :)