Question

If f(x)= 3x+6 which of the following is the inverse of f(x)

Answer 1

Answer:

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

Step-by-step explanation:

Replace f(x) with y and solve:

y = 3x + 6

Swap x and y

x = 3y + 6

Now isolate y

x/3 = 3y/3 + 6/3

1/3 x = y + 2

1/3 x - 2 = y + 2 - 2

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

Answer 2

For this case we have the following function:

$f (x) = 3x + 6$

We must find the inverse of the function, then:

Replace f (x) with y:$y = 3x + 6$

We exchange the variables:

$x = 3y + 6$

We solve for "y":

Subtracting 6 on both sides of the equation:

$x-6 = 3y$

Dividing between 3 on both sides of the equation:

$y = \frac {x} {3} - \frac {6} {3}\\y = \frac {x} {3} -2$

We change y by $f ^ {- 1} (x)$, and finally we have:

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

ANswer:

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