Find detailed and accurate answers to your questions on IDNLearn.com. Get the information you need from our community of experts who provide accurate and thorough answers to all your questions.
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.