Find the inverse of f(x)=5tan(3x+4)
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The first step in finding an inverse function is to write the function in “y equals” notation, as it will allow us simply to switch the variables and solve for us once again as follows:
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The inverse of the function f(x) = 5*tan(3x+4) is required.
Let y = f(x) = 5*tan(3x+4)
Now express x in terms of y
=> tan (3x + 4) = y/5
=> 3x + 4 = arc tan (y/5)
=> 3x = arc tan (y/5) - 4
=> x = [arc tan (y/5) - 4]/3
interchange x and y
y = f^-1(x) = [arc tan (x/5) - 4]/3
Let f(x) = y.
y = 5tan(3x+4)
First, we'll interchange x and y:
x = 5tan(3y+4)
We'll divide by 5:
x/5 = tan(3y+4)
3y + 4 = arctan (x/5)
We'll subtract 4 both sides:
3y = arctan (x/5) - 4
We'll divide by 3:
y = [arctan (x/5) - 4]/3
The requested inverse function is: f^-1(x) = [arctan (x/5) - 4]/3
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