Question 250480: whAT IS THE INVERSE OF THE ONE TO ONE FUNCTION f(X)= 6X-7 DIVIDED BY 5
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f(x) = (6x-7)/5
In this equation, solve for x.
multiply both sides of the equation by 5 to get:
5 * f(x) = 6x - 7
add 7 to both sides of this equation to get:
5 * f(x) + 7 = 6x
divide both sides of this equation by 6 to get:
(5 * f(x) + 7) / 6 = x
replace x with f(x) and replace f(x) with x (interchange them).
equation becomes:
(5 * x + 7) / 6 = f(x)
that's the same as:
f(x) = (5 * x + 7) / 6
that's your inverse function.
graph both equation to see that they are symmetric about the line y = x.
the graph looks like the lines are symmetric and reflections of each other about the line y = x so it appears that these are inverse functions.
test a point to see if they are symmetric about the line y = x.
If so, then the point (x,y) in one equation should be equal to the point (y,x) in the other equation.
try x = -15 the first equation.
at x = -15, y = (6x-7)/5 = -18
(x,y) = (-15,-18) in the first equation.
let x = -18 in the second equation. This is the value of y in the first equation.
at x = -18, y (5 * -18 / 6) = -15. This is the value of x in the first equation.
(y,x) = (-18,-15) in the second equation.
the point (x,y) = (-15,-18) in the first equation is equal to the point (y,x) = (-18,-15) in the second equation so the lines are symmetric about the line y = x.
in the equations above, if you let y = f(x), then where I have used y you can substitute f(x), and where I have used f(x) you can substitute y, as necessary, in order to put the equation in the form that you need.
They both mean the same thing.
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