F(x)=3x+2 inverse functions

Question

I don't know what to put here its on a work sheet I need help I hate math

Answer 1

f(x) = 3x +2

x = 3f^-1(x) + 2     subtract 2 from both sides

x - 2 = 3f^-1(x)      divide both sides by 3

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

Answer 2

Let's for the moment call F(x) the variable y instead:

y = 3x + 2

The inverse function means that we switch the places of the y and x and then solve for y (in other words, isolate y):

x = 3y + 2

 

Step one, move the constant to the other side. In this case, we need to subtract two to both sides:

x - 2 = 3y + 2 - 2

x - 2 = 3y

 

Step two, isolate the variable y, so we need to divide both sides by 3:

(x - 2) / 3 = 3y / 3

^{(x - 2)} / ₃ = y

 

We can also then distribute that 3 to our numerator:

¹/₃x - ²/₃ = y

 

Now we replace the y with the F(x) from the beginning, but since we're using the inverse of the function here, we use a -1 power:

F^-1(x) = ¹/₃ - ²/₃

Answer 3

F(x)=3x+2

let x=4

F(4)=3*4+2

F(4)=12+2

F(4)=14

let y=3x+2

when x=4, y=14

14=3x+2

14-2=3x

(14-2)/3=x

replace 14 with y

(y-2)/3=x