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Question 82159: I don't know how to do this one. My teacher doesn't use the book to teach and he usually makes up his own problems. The book defines inverse of a function but I don't understand what it is trying to say, this stuff confuses me so much...
Find the inverse of f(x)=-2x^-1+3 and prove it's the inverse.
I know it has to do with f^-1 but I just don't understand where to plug this stuff in and how to solve it.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the inverse of f(x)=-2x^-1+3 and prove it's the inverse
Interchange x and y to get:
x = -2y^-1 +3
Solve for y to get:
2y^-1 = -x+3
y^-1 = (-x+3)/2
Invert both sides to get:
y = 2/(3-x)
That is the inverse, usually called f^-1(x).
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Show it is an inverse:
f^-1[f(x)] = f^-1[-2x^-1+3] = f^-1[(-2+3x)/x] = 2/[3-[(-2+3x)/x]]
= 2/[(3x+2--3x)/x
= 2x/2
=x
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Reminder: f(x)=-2x^-1+3
f[f^-1(x)] = f[2/(3-x)]
= -2(2/(3-x))+3
=-3+x+3
=x
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Since f[f^-1(x)] = x
and
Since f[f^-1(x)]=x
f and f^-1 are inverse to one another.
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Cheers,
Stan H.
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