The inverse of an equation is found by switching \(x\) and \(y\).
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OpenStudy (kittiwitti1):
So if you have an equation that says that \(y=3x+4\), your inverse will be \(x=3y+4\). But you still have to find the y-value
OpenStudy (kittiwitti1):
Here you are given \(f(x)=2x-10\), also known as \(y=2x-10\).
If you switch the \(x\) with the \(y\) you would get \(x=2y-10\).
Now you need to find what \(y\) by itself is.
OpenStudy (kevin):
You need to to make equation of x from y =2x - 10.
Can you do it?
OpenStudy (kittiwitti1):
Your first step to isolating/finding what \(y\) is would be to get \(2y\) alone and \(x\) on the other side:\[\cancel{x}\cancel{-x}-2y=\cancel{2y}\cancel{-2y}-10-x\]\[-2y=-10-x\]
OpenStudy (itzmee):
wait so my answer is "True"?
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OpenStudy (kittiwitti1):
Well, did you solve for the inverse?
OpenStudy (itzmee):
yes, i got \[f -\prime (x) = 5+ \frac{ x }{ 2}\]
OpenStudy (itzmee):
@kittiwitti1
OpenStudy (kittiwitti1):
What is that
OpenStudy (kittiwitti1):
f-`(x) lol
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OpenStudy (itzmee):
f^-1
OpenStudy (kittiwitti1):
Oh, this?\[\Large{f^{-1}(x)}\]
Anyway, you got it right ☺ good job