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