Question

What is the inverse of the function f(x)=3x-2

Answer 1

For this case we must determine the inverse of the following function:

$f (x) = 3x-2$

Step 1:

We write $y = f (x)$

$y = 3x-2$

Step 2:

We clear x:

$y + 2 = 3x\\\frac {y + 2} {3} = x$

Step 3:

"x" and "y" are exchanged:

$y = \frac {x + 2} {3}$

The inverse is:

$f ^ {- 1} (x) = \frac {x + 2} {3}$

ANswer:

$f ^ {- 1} (x) = \frac {x + 2} {3}$

Answer 2

Answer:

f⁻¹(x) = x+2 / 3

Step-by-step explanation:

Given function is:

f(x) = 3x-2

We  have to find the inverse of given function.

Put y = f(x)  in given function, we have

y =3x-2

Adding 2 to both sides of above equation , we have

y+2 = 3x-2+2

y+2 = 3x

Dividing by 3 to both sides of above equation, we have

y+2 / 3 = 3x / 3

y+2 / 3 = x

Put x = f⁻¹(y) in above equation , we have

y+2 / 3 = f⁻¹(y)

Swapping equation , we have

f⁻¹(y) = y+2 / 3

Replace y with x , we have

f⁻¹(x) = x+2 / 3   which is the answer.