Let $\mathrm{f}\left(\mathrm{x}\right)=3{\mathrm{x}}^2-7\mathrm{x}+\mathrm{c}$, where c is a variable coefficient and $\mathrm{x}>\frac{7}{6}$. Then the value of [c] such that f(x) touches f^-1(x) is (where $[\cdot ]$ represents greatest integer function) ___. 

f(x) and f^-1(x) can only intersect on the line y = x and, therefore, y = x must be tangent at the common point of tangency. Hence, 

$3{\mathrm{x}}^2-7\mathrm{x}+\mathrm{c}=\mathrm{x}$

or $3{\mathrm{x}}^2-8\mathrm{x}+\mathrm{c}=0$                (1)

This equation must have equal roots. Therefore,

$64-12\mathrm{c}=0$

or $\mathrm{c}=\frac{64}{12}=\frac{16}{3}$