Question 1118646
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I don't know a formal way for finding f(x) from the given information.  Perhaps another tutor will also respond with a different method than I use.<br>
For me, f(3x-2) = x+5 means that f(x) is of the form {{{f(x) = (x/3)+b}}}.<br>
To find b, use the given fact that f(3x-2) = x+5:<br>
{{{f(3x-2) = (3x-2)/3 + b = x+5}}}
{{{x-2/3+b = x+5}}}
{{{b = 5+2/3 = 17/3}}}<br>
So<br>
{{{f(x) = (x/3)+17/3}}}<br>
Then<br>
{{{f(7) = 7/3 + 17/3 = 24/3 = 8}}}<br>
To find f^-1(7), set f(x)=7 and solve for x:<br>
{{{7 = (x/3)+17/3}}}
{{{4/3 = x/3}}}
{{{x = 4}}}<br>
Finally, then, f(7)+f^-1(7) = 8+4 = 12.