Math
posted by Girly Girl
The function f(x)=(x5)^2+2 is not onetoone. Identify a restricted domain that makes the function onetoone, and find the inverse function.
a. restricted domain: x>or=5; f^1(x)=5sqrt(x2)
b. restricted domain: x>or=5; f^1(x)=5+sqrt(x2)
c. restricted domain: x<or=5; f^1(x)=5+sqrt(x+2)
d. restricted domain: x<or=5; f^1(x)=5+sqrt(x2)
I really need help if someone could please explain this to me, I would greatly appreciate it. Thank you!

Steve
the axis of symmetry is the line x=5
So, any domain on one side of that line will be onetoone.
Now, for the inverse, swap variables and solve for f^1
x = (f5)^2+2
x2 = (f5)^2
f5 = ±√(x2)
f = 5±√(x2)
Now, we need one branch only, but √(x2) is only defined for x>=2
On the original parabola, the right branch is x>=5. So, only A or B is a candidate, and so B is the choice.
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