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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)_________ |
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Answer» Correct Answer - 5 `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)` |
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