Let f ( x ) = 3 x 2 − 7 x + c , where 'c' is a variable co-efficient and x 6 7 . The value of 'c' such that f ( x ) touches f − 1 ( x ) is......

Question

Let f ( x ) = 3 x 2 − 7 x + c , where 'c' is a variable co-efficient and x > 6 7 ​ . The value of 'c' such that f ( x ) touches f − 1 ( x ) is......

TestHub · Accepted Answer

f ( x ) and f − 1 ( x ) can only intersect on the line y = x ∴ y = x must be tangent Solving 3 x 2 − 7 x + c = x p ⇒ 3 x 2 − 8 x + c = 0 The above equation has real and equal roots ​ ⇒ 64 − 12 c = 0 ​ c = 3 16 ​ ​

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