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The inverse function of the given functions are and
=-2x+6.
The given functions are f(x)=4(x-1) and g(x)=(6-x)/2.
We need to determine and
.
In mathematics, an inverse is a function that serves to “undo” another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.x. A function f that has an inverse is called invertible and the inverse is denoted by .
Now, we can write f(x)=4(x-1) as y=4x-4
To find the inverse, interchange the variables and solve for y.
That is, x=4y-4
⇒x=4(y-1)
⇒(y-1)=x/4
⇒y=x/4 +1
⇒
We can write g(x)=(6-x)/2 as y=(6-x)/2.
To find the inverse, interchange the variables and solve for y.
That is, x=(6-y)/2
⇒2x=6-y
⇒y=-2x+6
⇒=-2x+6
Therefore, the inverse function of the given functions are and
=-2x+6.
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