Question

Find the inverse of f(x)=5tan(3x+4)

Accepted Answer

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

Answer

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 inverse trig function, (also seen as sin^-1):
 
3x+4=arctan(x/5)
 
3x=arctan(x/5)-4
 
x=(arctan(x/5)-4)/3
 
Now, finally, we can replace y with x and vice verse:
 
y=(arctan(x/5)-4)/3

If you have access to a graphing utility (such as the one linked below), the try to graph both the original and new (inverse) function to see the relationship. Hint: it is simply a reflection around the line y=x In this case, make sure you are graphing in radian mode.

Answer

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

algebra1

Find the inverse of f(x)=5tan(3x+4)

Expert Answers info

Unlock This Answer Now

Related Questions

Student Answers

Ask a Question

Popular Questions