I have a question which asks "Verify that inverse g(x) = g(x)" with the fractions g(x)=(x+1)/(x-1)
I am drawing a blank is all I can think of is showing that they are inverse of each other which isn't what the question is asking for
+129840 It's asking you to show that g(x) is it's own inverse
Fof g(x), write y and we have
y = ( x + 1) /(x - 1) the object is to first get a single x by itself......multiply both sides by x - 1
y ( x - 1) = x + 1
yx - y = x + 1 rearrange as
xy - x = y + 1 factor out x on the left
x(y - 1) = y + 1 divide both sides by y - 1
x = [ y + 1 ] / [ y - 1] "exchange" x with y
y = [x + 1 ] / [x - 1] and for y, write g-1(x)
g-1(x) = [x + 1 ] / [x - 1] notice that this is the same as g(x)
