Find the inverse of the function f(x) = -2ln(2x-3) + 2.
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Given the function f(x) = -2ln(2x-3) + 2
We need to find the inverse function f^-1 (x).
Let us assume that f(x) = y
==> y= -2ln(2x-3) + 2
The goal is to isolate x on one side .
Let us subtract 2 from both sides.
==> y-2 = -2ln(2x-3)
Now we will divide by -2
==> (y-2)/-2 = ln (2x-3)
Now we will rewrite using the exponent form:
==> 2x-3 = e^(2-y)/2
Now we will add 3 to both sides.
==> 2x = e^(2-y)/2 + 3
Now we will divide by 2.
==> x = [ e^(2-y)/2 + 3] / 2
Now we will replace y and x.
==> y= [ e^(2-y)/2 + 3 ] / 2
Then the inverse function is f^-1 (x) = [ e^(2-y)/2 + 3] / 2
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calendarEducator since 2010
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starTop subjects are Math, Science, and Business
We have the function f(x) = -2ln(2x-3) + 2
Let y = f(x) = -2*ln (2x - 3) + 2
=> y - 2 = -2*ln (2x - 3)
=> -(y-2)/2 = ln (2x - 3)
=> e^ ( (2-y)/2)) = 2x - 3
=> 2x = 3 + e^( (2-y)/2))
=> x = [3 + e^( (2-y)/2))]/2
=> x = 3/2 + e^(1 - y/2)/2
interchange x and y , we get the inverse function as f(x) = 3/2 + e^(1 - x/2)/2.
Therefore the required inverse is f(x) = 3/2 + e^(1 - x/2)/2.
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