Question

Given the function p(x)= x²-6x+5 and q(x) =2x-7Find the function p‐¹(x) ​.

Answer 1

To find the inverse of the function, swap x and y, and solve for y.

Step-by-step explanation:

To find the inverse of a function, we swap the roles of x and y and solve for y. So, for the function p(x) = x² - 6x + 5, let's swap x and y to get x = y² - 6y + 5. Now, we solve for y:

x = y² - 6y + 5

0 = y² - 6y + 5 - x

0 = y² - 6y + (5 - x)

Using the quadratic formula, we have:

y = (-(-6) ± √((-6)² - 4(5 - x)))/(2(1))

y = (6 ± √(36 - 4(5 - x)))/(2)

y = (6 ± √(x² - 10x + 16))/(2)

y = (6 ± (x - 4))/(2)

y = (x - 4)/2 or y = (-x + 8)/2

Therefore, the function p⁻¹(x) is p⁻¹(x) = (x - 4)/2 or p⁻¹(x) = (-x + 8)/2.