How to Solve for the Inverse Function of f(x) = 5x + 4 – 6 when x = 19?

To find the inverse function of f(x) = 5x + 4 – 6 when x = 19, we will first simplify the function and then solve for its inverse.

First, let’s rewrite the function:

• f(x) = 5x – 2

Next, to find the inverse, we replace f(x) with y:

• y = 5x – 2

Now, we need to swap x and y:

• x = 5y – 2

Next, we will solve for y:

1. Add 2 to both sides: x + 2 = 5y
2. Now, divide both sides by 5: y = (x + 2) / 5

Thus, the inverse function is:

• f^-1(x) = (x + 2) / 5

Finally, to find the value of the inverse function when x = 19, we substitute 19 into the inverse function:

• f^-1(19) = (19 + 2) / 5 = 21 / 5 = 4.2

So, the value of the inverse function when x = 19 is 4.2.