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

The inverse of a function is the opposite of the function.

The inverse of the function is: $\mathbf{f^{-1}(x) =\frac{ x + 2}{3}}$

The function is given as:

$\mathbf{f(x) = 3x - 2}$

Express as:

$\mathbf{y = 3x - 2}$

Swap x and y

$\mathbf{x = 3y - 2}$

Add 2 to both sides

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

Divide both sides by 3

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

Rewrite as:

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

Hence, the inverse of the function is: $\mathbf{f^{-1}(x) =\frac{ x + 2}{3}}$

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