Inverse functionWhat is the inverse formula for the function f(x)= 3x-7

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to find the equation of inverse function, hence, you may use the equation that relates the function and its inverse, such that:

`(fof^(-1))(x) = x`

`f(f^(-1)(x)) = x`

Substituting `f^(-1)(x)` for x in equation of `f(x)` yields:

`3f^(-1)(x) - 7 = x => 3f^(-1)(x) = x + 7 => f^(-1)(x) = (x + 7)/3`

Hence, evaluating the equation of inverse function, yields `f^(-1)(x) = (x + 7)/3.`

giorgiana1976 | Student

To determine the inverse function means to determine x with respect to y, from the given expression of f(x).

We'll note f(x) = y and we'll re-write the equation:

y = 3x - 7

We'll use the symmetryc property:

3x - 7 = y

We'll isolate 3x to the left side. For this reason, we''' add 7 both sides:

3x = y + 7

Now, we'll divide by 3 both sides to get x

x = (y+7)/3

The inverse function is f(y) = (y+7)/3

By definition, we'll write the inverse function as:

f^-1(x) = (x+7)/3

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