SOLUTION: find the inverse of f(x) = 7x

SOLUTION: find the inverse of f(x) = 7x - 2

Question 288600: find the inverse of f(x) = 7x - 2
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
To find the inverse function of f(x), you solve for x and then you replace x with f(x) and you replace f(x) with x.

Your equation is:

f(x) = 7x - 2

Solve for x.

Add 2 to both sides of this equation to get:

f(x) + 2 = 7x

Divide both sides of this equation by 7 to get:

(f(x) + 2)/7 = x

Since, in general, a = b implies that b = a, this equation becomes:

x = (f(x) + 2)/7

Replace x with f(x) and replace f(x) with x to get:

f(x) = (x+2)/7

That's your inverse function.

Graph both your function and your inverse function.

Set y = f(x) to get:

y = 7x - 2 (your regular function).

y = (x+2)/7 (your inverse function).

Graph also the function y = x.

Your graph looks like this:

Your function and your inverse function should be symmetric about the line y = x.

In the graph, they look like they are symmetric, so that's a step in the right direction.

To prove they are symmetric, you need to take any value of x in your original function and solve for f(x).

Let x = 3.

Your original function is f(x) = 7x-2.

That gets you f(x) = 7*3 - 2 = 21-2 = 19.

The coordinate points of your original equation are (x,y) = (3,19).

Now take f(x) from your original equation and replace x in your inverse function with it to get:

f(x) = (x+2)/7 becomes:

f(19) = (19+2)/7 = 21/7 = 3.

When x is equal to 19 in your inverse function, f(x) = 3.

The coordinate points for your inverse function are (x,y) = (19,3).

You have:

When x = 3 in your original function, (x,y) = (3,19).

When x = 19 in your inverse function, (x,y) = (19,3).

This proves that the functions are inverse functions of each other, because the inverse function undoes what the regular function does.

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