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:

Let y=5*tan(3x+4)
Now switch x and y:
x=5*tan(3y+4)
Now solve for y algebraically using the conventional order of operations:
x/5=tan(3x+4)
Now take the...

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giorgiana1976 | Student

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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