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lifewmylilweeb:
@joe348
Extrinix:
So it's easier to convert \(f(x)=zx+b\) to inverse than it is to convert \(f^{-1}(x)=zx=b\)
Let's start off with \(f(x)=2x-8\)
Understand that we need to switch y and x, then solve for y.
\(y=2x-8\)
Swap them
\(x=2y-8\)
Now solve the equation, what would you get?
lifewmylilweeb:
\[\frac{ x+8 }{ 2}\]
lifewmylilweeb:
so the first one goes with the second one
Extrinix:
Which would give you \(\dfrac{1}{2}x+4\), which is your inverse
Inverse:
\(f^{-1}(x)=\dfrac{1}{2}x+4\)
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Extrinix:
Correct ^^
Extrinix:
Most teachers don't force you to simplify completely, but knowing how to simplify it completely could help if there's a question that asks for it...
Extrinix:
Anyways, onto #2
\(f(x)=2x+7\)
Swap x and y then solve for y, as the other one was
\(x=2y+7\)
What would you get?