what is the inverse fumction of f(x)=2x/3-17

Question

a.)f^-1=5x

b.)f^-1=x^3/2

c.)f^-1=x+10

d.)f^-1=3(x+17)/2

 

Answer 1

Finding the inverse of a function is pretty straightforward, always using a standard procedure.

 

f(x)=2x / 3 - 17

 

1. Change "f(x)" to "y" to make it easier to do the math:

 

y = 2x / 3 - 17

 

2. Switch x and y:

 

x = 2y / 3 - 17

 

3. Solve for y in the new equation:

 

x = 2y / 3 - 17

x + 17 = 2y / 3

3 (x + 17) = 2y

3 (x + 17) / 2 = y

 

4. Change "y" to "f^-1(x)"

 

3 (x + 17) / 2 = f^-1(x)

 

f^-1(x) = 3 (x + 17) / 2

 

 

So the answer is d.

 

 

Answer 2

Your answer would be D.

 

The setup is simple. replace f(x) with y=(2x/3)-17. The switch the x and y to where you now have x=(2y/3)-17.

 

Now solve for y:     x=(2y/3)-17              Add 17 to both sides.

                             x+17=(2y/3)            Multiply both sides by 3.

                            3(x+17)=2y              Now divide both sides by 2 to get Y by itself.

                            3(x+17)/2=y             Now replace y with f^-1

                            f^-1=3/(x+17)/2       Final Answer