Question

Find the inverse of F(x)=
`5x^(2) -10x+7`

Answer 1

So the inverse of F(x) is F^-1(x) = 1 ± sqrt((x-2)/5).

Explanation:

To find the inverse of F(x), we need to follow these steps:

Step 1: Replace F(x) with y:

y = 5x^2 - 10x + 7

Step 2: Solve for x in terms of y:

y = 5x^2 - 10x + 7

y - 7 = 5x^2 - 10x

5x^2 - 10x = y - 7

5(x^2 - 2x) = y - 7

Completing the square:

5(x^2 - 2x + 1) = y - 7 + 5

5(x - 1)^2 = y - 2

x - 1 = ±sqrt((y-2)/5)

x = 1 ± sqrt((y-2)/5)

Step 3: Replace x with F^-1(x):

F^-1(x) = 1 ± sqrt((x-2)/5)

So the inverse of F(x) is F^-1(x) = 1 ± sqrt((x-2)/5).