Let `f(x)=3x^2-7x+c ,` where `c` is a variable coefficient and `x >7/6` . Then the value of `[c]` such that `f(x)` touches `f^(-1)(x)` is (where [.] represents greatest integer function)_________

Answer

5

Explanation

`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,
` 3x^(2)-7x+c=x`
` or 3x^(2) -8x+c=0 " (1)" `
This equation must have equal roots. Therefore,
`64-12c =0`
`or c=(64)/(12)=(16)/(3)`