Find the inverse of the following functions f(x)=6-3x g(x)=x+2
2 answers:
f(x) = -3x + 6
y = -3x + 6
x = -3y + 6
x - 6 = -3y
-3 -3
⁻¹/₃x + 2 = y
⁻¹/₃x + 2 = f⁻¹(x)
g(x) = x + 2
y = x + 2
x = y + 2
x - 2 = y
x - 2 = g⁻¹(x)
Problem 1:
![y=f\left( x \right) ,\\ \\ y=6-3x\\ \\ 3x=6-y\\ \\ x=\frac { 6 }{ 3 } -\frac { y }{ 3 } \\ \\ x=2-\frac { 1 }{ 3 } y\\ \\ \therefore \quad { f }^{ -1 }\left( x \right) =2-\frac { 1 }{ 3 } x](https://tex.z-dn.net/?f=y%3Df%5Cleft%28%20x%20%5Cright%29%20%2C%5C%5C%20%5C%5C%20y%3D6-3x%5C%5C%20%5C%5C%203x%3D6-y%5C%5C%20%5C%5C%20x%3D%5Cfrac%20%7B%206%20%7D%7B%203%20%7D%20-%5Cfrac%20%7B%20y%20%7D%7B%203%20%7D%20%5C%5C%20%5C%5C%20x%3D2-%5Cfrac%20%7B%201%20%7D%7B%203%20%7D%20y%5C%5C%20%5C%5C%20%5Ctherefore%20%5Cquad%20%7B%20f%20%7D%5E%7B%20-1%20%7D%5Cleft%28%20x%20%5Cright%29%20%3D2-%5Cfrac%20%7B%201%20%7D%7B%203%20%7D%20x)
Problem 2:
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Step-by-step explanation:
it is shown in the above process.
hope you understand