Question

Having trouble with this question on my assignment. I got the rest answered.

Assume a domain A = {x ∈ ℝ | x ≥ 2} for the function f(x) = x^2 − 4x + 2 .

Find the value of the inverse f^-1(x) at x = 5. Provide 4 decimal places.

I'm getting 5.0000 but I'm sure that it's wrong.

Answer 1

y = x^2-4x+2
parabola upright, holds water. Therefore it is single valued in its range but the inverse is not single valued (not a function)

If x = 2, y = -6

now what does the inverse look like?

x = y^2 -4y + 2
now if x = 5 then
y^2 - 4 y - 3 = 0
y = [ 4 +/- sqrt(16+12) ]/2
y = [4 +/- 5.2915 ]/2
y = 4.6458 or -.6458