Question

And the inverse of f(x) = 3x²-5x+7
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Answer 1

inverse of the function x² - 3x + 7 is [5 ± √(12x - 59)] /6.

Explanation:

Let f(x) = y → f-¹y = x → g(y) = x

We need a function g which gives x for g(y).

=> f(x) = y

=> 3x² - 5x + 7 = y

=> x² - x(5/3) + (7/3) = y/3

=> x² - 2x(5/6) + (7/3) = y/3

=> x² - 2x(5/6) + (5/6)² + (7/3) = y/3 + (5/6)²

=> (x - 5/6)² + 7/3 = (y/3 + 25/36)

=> (x - 5/6)² = y/3 + 25/36 - 7/3

=> (x - 5/6)² = (12y + 25 - 84)/36

=> x - 5/6 = ± √(12y - 59) /6

=> x = [ 5 ± √(12y - 59) ]/6

=> x = g(y)

Hence, inverse of the function x² - 3x + 7 is [5 ± √(12x - 59)] /6.