Question 1209327
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(1) for tutor @ikleyn -- you have a wrong sign in your original equation....<br>
(2) The comments from tutor @ikleyn that there is no need to find the inverse function to answer this question are correct.<br>
(3) In a problem where you are in fact asked to find the inverse of a rational function, it is useful to know that the inverse of<br>
{{{y=(ax+b)/(cx+d)}}}<br>
is<br>
{{{y=(-dx+b)/(cx-a)}}}<br>
(Note the pattern: the "b" and "c" stay where they are; the "a" and "d" switch places and both change sign.)<br>
For this problem, given<br>
{{{y=(2x+5)/(x-4)}}}<br>
the inverse is<br>
{{{y=(4x+5)/(x-2)}}}<br>
So<br>
ANSWER: {{{f^(-1)(1)=(4+5)/(1-2)=9/-1}}} = -9<br>