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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