For a given function f(x) we define the domain restrictions as values of x that we can not use in our function. Also, for a function f(x) we define the inverse g(x) as a function such that:
g(f(x)) = x = f(g(x))
<u>The restriction is:</u>
x ≠ 4
<u>The inverse is:</u>
![y = 4 + \sqrt{\frac{11}{x} }](https://tex.z-dn.net/?f=y%20%3D%204%20%2B%20%5Csqrt%7B%5Cfrac%7B11%7D%7Bx%7D%20%7D)
Here our function is:
![f(x) = \frac{11}{(x - 4)^2}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B11%7D%7B%28x%20-%204%29%5E2%7D)
We know that we can not divide by zero, so the only restriction in this function will be the one that makes the denominator equal to zero.
(x - 4)^2 = 0
x - 4 = 0
x = 4
So the only value of x that we need to remove from the domain is x = 4.
To find the inverse we try with the general form:
![g(x) = a + \sqrt{\frac{b}{x} }](https://tex.z-dn.net/?f=g%28x%29%20%3D%20a%20%2B%20%5Csqrt%7B%5Cfrac%7Bb%7D%7Bx%7D%20%7D)
Evaluating this in our function we get:
![g(f(x)) = a + \sqrt{\frac{b}{f(x)} } = a + \sqrt{\frac{b*(x - 4)^2}{11 }}\\\\g(f(x)) = a + \sqrt{\frac{b}{11 }}*(x - 4)](https://tex.z-dn.net/?f=g%28f%28x%29%29%20%3D%20a%20%2B%20%5Csqrt%7B%5Cfrac%7Bb%7D%7Bf%28x%29%7D%20%7D%20%20%3D%20a%20%2B%20%5Csqrt%7B%5Cfrac%7Bb%2A%28x%20-%204%29%5E2%7D%7B11%20%7D%7D%5C%5C%5C%5Cg%28f%28x%29%29%20%3D%20a%20%2B%20%5Csqrt%7B%5Cfrac%7Bb%7D%7B11%20%7D%7D%2A%28x%20-%204%29)
Remember that the thing above must be equal to x, so we get:
![g(f(x)) = a + \sqrt{\frac{b}{11 }}*(x - 4) = x\\\\{\frac{b}{11 }} = 1\\{\frac{b}{11 }}*4 - a = 0](https://tex.z-dn.net/?f=g%28f%28x%29%29%20%3D%20a%20%2B%20%5Csqrt%7B%5Cfrac%7Bb%7D%7B11%20%7D%7D%2A%28x%20-%204%29%20%3D%20x%5C%5C%5C%5C%7B%5Cfrac%7Bb%7D%7B11%20%7D%7D%20%3D%201%5C%5C%7B%5Cfrac%7Bb%7D%7B11%20%7D%7D%2A4%20-%20a%20%3D%200)
From the two above equations we find:
b = 11
a = 4
Thus the inverse equation is:
![y = 4 + \sqrt{\frac{11}{x} }](https://tex.z-dn.net/?f=y%20%3D%204%20%2B%20%5Csqrt%7B%5Cfrac%7B11%7D%7Bx%7D%20%7D)
If you want to learn more, you can read:
brainly.com/question/10300045
Answer:
127/12
Step-by-step explanation:
4 × 2 + 12x = 135
(1. Simplify 4 x 2 to 8.
8 + 12x = 135
(2. Subtract 88 from both sides.
12x= 135 - 8
(3. Simplify 135 - 8 to 127
12x = 127
(4. Divide both sides by 12
x= 127/12
Decimal Form: 10.583333
I think this is the awnser, but don't quote me on that
I think you can use, LA= (perimeter of base • slant height of pyramid)/ 2. I’m probably wrong but see if that helps.
The answer is x = 3, as we know that the measure of vertical angles are equal. This means that 2x = x + 3, so x = 3.<span />
Bbbbbbbbbbbbbbbbbbbbb is the answer