SOLUTION: f : x —> (2x + 7) / (x-2) for x ∈ R , x ≠ 2 a) find an expression of f^-1 (x) b) State what your answer to part (a) tells you about the symmetry of the graph of y = f(x).

Algebra ->  Test -> SOLUTION: f : x —> (2x + 7) / (x-2) for x ∈ R , x ≠ 2 a) find an expression of f^-1 (x) b) State what your answer to part (a) tells you about the symmetry of the graph of y = f(x).      Log On


   

Question 1200540: f : x —> (2x + 7) / (x-2) for x ∈ R , x ≠ 2
a) find an expression of f^-1 (x)
b) State what your answer to part (a) tells you about the symmetry of the graph of y = f(x).
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i solved for the inverse equation and it turns out that the inverse equation is the same as the regular equation.
here's how i did it.
start with y = (2x+7) / (x-2)
replace y with x and x with y to get:
x = (2y+7) / (y-2)
now you want to solve for y.
multiply both sides of the equation by (y-2) to get:
x * (y-2) = 2y+7
simplify to get:
yx - 2x = 2y + 7
add 2x to both sides of the equation and subtract 2y from both sitdes of the equation to get:
yx - 2y = 2x + 7
factor out the y on the left side of the equation to get:
y * (x-2) = 2x + 7
divide both sides of the equation by (x-2) to get:
y = (2x+7)/(x-2)
the inverse equation is the same as the regular equation *****
since the inverse equation is symmetric to the original equation about the line y = x, this says that the original equation is symmetric about the line y = x.
a graph of the original equation should show this to be true.
that's the only conclusion i can draw from this, since i can't think of anything else.
here's the graph.

i found a reference that seems to talk about this.
it can be found at https://math.stackexchange.com/questions/541978/can-the-inverse-of-a-function-be-the-same-as-the-original-function
the reference calls it an involution.