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).
B, I took this test recently and got it right
Answer:
The error interval for x is:
[3.65,3.74]
Step-by-step explanation:
The number after rounding off is obtained as:
3.7
We know that any of the number below on rounding off the number to the first decimal place will result in 3.7:
3.65 3.66 3.67 3.68 3.69 3.70 3.71 3.72 3.73 3.74
( Because if we have to round off a number present in decimals to n place then if there is a number greater than or equal to 5 at n+1 place then it will result to the one higher digit at nth place on rounding off and won't change the digit if it less than 5 )
Hence, the error interval is:
[3.65,3.74]
Okay, here we have this:
Considering the provided information, we are going to find the x- and y- intercepts and explain its meaning. So we obtain the following:
Since the x-intercept is the point where the Graph intersects the x-axis (y=0) and the y-intercept is the point where the Graph intersects the y-axis (x=0), we have that:
x-intercept=(300, 0)
y-intercept=(0, 16)
Since the y-axis represents the number of gallons, and the x-axis time, then the y-intercept indicates that when filling the tank it was left with 16 gallons, and the x-intercept indicates that when emptying the tank had traveled 300 miles.