It’s 56 UwU
That’s your answer
Answer:
To find f-¹(x) of f(x) equate f(x) to y
That's
f(x) = y
So we have
![y = \frac{4x - 7}{10}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B4x%20-%207%7D%7B10%7D%20)
Next interchange the variables that's x becomes y and y becomes x
That's
![x = \frac{4y - 7}{10}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B4y%20-%207%7D%7B10%7D%20)
Next make y the subject
Cross multiply
We have
4y - 7 = 10x
Move -7 to the right side of the equation
4y = 10x + 7
Divide both sides by 4
We have the final answer as
![y = \frac{10x + 7}{4}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B10x%20%2B%207%7D%7B4%7D%20)
So
![f ^{ - 1} (x) = \frac{10x + 7}{4}](https://tex.z-dn.net/?f=f%20%5E%7B%20-%201%7D%20%28x%29%20%3D%20%20%5Cfrac%7B10x%20%2B%207%7D%7B4%7D%20)
Hope this helps you
![-x-2y=-4 \\ 3x+y=12 \\ \\ \hbox{the first equation:} \\ -x-2y=-4 \ \ \ \ \ \ |+2y \\ -x=2y-4 \ \ \ \ \ \ \ \ |\times (-1) \\ x=-2y+4](https://tex.z-dn.net/?f=-x-2y%3D-4%20%5C%5C%203x%2By%3D12%20%5C%5C%20%5C%5C%20%5Chbox%7Bthe%20first%20equation%3A%7D%20%5C%5C%20-x-2y%3D-4%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%7C%2B2y%20%5C%5C%20-x%3D2y-4%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%7C%5Ctimes%20%28-1%29%20%5C%5C%20x%3D-2y%2B4)
The expression you would substitute for x is -2y+4. The answer is d.
the commutative property was used
Step-by-step explanation:
We know that tan=sin/cos, so tan(x+π/2)=
![\frac{sin(x+pi/2)}{cos(x+pi/2)}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%28x%2Bpi%2F2%29%7D%7Bcos%28x%2Bpi%2F2%29%7D)
Then, we know that sin(u+v)=sin(u)cos(v)+cos(u)sin(v),
so our equation is then
Then, cos(u+v)=cos(u)cos(v)-sin(u)sin(v), so our expression is then
![\frac{cos(x)}{cos(x)cos(\pi/2)-sin(x)sin(\pi/2)} = \frac{cos(x)}{-sin(x)} = -cot(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%28x%29%7D%7Bcos%28x%29cos%28%5Cpi%2F2%29-sin%28x%29sin%28%5Cpi%2F2%29%7D%20%3D%20%5Cfrac%7Bcos%28x%29%7D%7B-sin%28x%29%7D%20%3D%20-cot%28x%29)