Domain refers to the x values that the function occupies, and range referring to the y values. For example: A function of 1/x does not have any values of x=0 or y=0 because these are the asymptotes of the equation.
Therefore... for every value of A to map to set B, the domain and range must specify this i.e:
Domain: x ∈ R, x ≠0
Range: y ∈ R, y ≠0
Now every element from set A maps to elements in set B and the equation f(x) = 1/x {x ∈ R, x ≠0} and is now a function.
It is regarded as a one-to-one function because every element of the range comes exactly from one element in the domain.
Finding the inverse of a function:
The example function will be: 2x²-7
1.Set the function equal to y:
It is regarded as a one-to-one function because every element of the range comes exactly from one element in the domain.
Finding the inverse of a function:
The example function will be: 2x²-7
1.Set the function equal to y:
y=2x²-7
2.Rearrange to make x the subject:
y=2x²-7
y+7=2x²
0.5(y+7)=x²
x=√(0.5(y+7))
3.Replace (x=) with (f-1(x)=) and replace (y) with (x)
x=√(0.5(y+7))
f-1(x)=√(0.5(y+7))
f-1(x)=√(0.5(x+7))
The inverse of a function graphically, is literally just f(x) reflected in the line y=x.
For example:
"https://en.wikipedia.org/wiki/Inverse_function#/media/File:Inverse_Function_Graph.png"
As shown above, the function just gets reflected in the line y=x to give the inverse function.
