Question 882022
{{{y="f(x)" = (3x + 7)/(4x - 9) }}}, show that {{{x = "f(y)"}}}
<pre>
Sorry but that is just not true in general.  

Here is a disproof by a counterexample.

If it were true in general it would be true if x = 1

Suppose x = 1

{{{y="f(x)" = (3x + 7)/(4x - 9) }}}

{{{y="f(1)" = (3(1) + 7)/(4(1) - 9) }}}

{{{y="f(1)" = (3 + 7)/(4 - 9) }}}

{{{y="f(1)" = 10/(-5) }}}

{{{y="f(1)" = -2 }}}

Now in order for what we are asked to prove to be true in this
case, we must end up with

{{{x = "f(y)"}}}, which in this case would be

{{{1 = "f(-2)"}}}

However f(-2) is found by substituting x=-2 in

{{{y="f(x)" = (3x + 7)/(4x - 9) }}}

{{{-2=f(-2) = (3(-2) + 7)/(4(-2) - 9) }}}

{{{-2=f(-2) = (-6 + 7)/(-8 - 9) }}}

{{{-2=f(-2) = 1/(-17) }}}

{{{-2=f(-2) = -1/17 }}}

which is false.  So what you were asked to
prove is not true.

Edwin</pre>