Question

Which of the following identifies the quadratic function that is related to the square root function m(x)=x−2−−−−√+4
?(1 point)

n(x)=(x+4)2−2


n(x)=14x2+2


n(x)=(x−4)2+2


n(x)=4x2+2

Answer 1

n(x) = (x − 4)^2 + 2.

Reason: Let y = √(x − 2) + 4. Swap x and y to find the inverse: x = √(y − 2) + 4 → √(y − 2) = x − 4 → y − 2 = (x − 4)^2 → y = (x − 4)^2 + 2. (Domain of this inverse is x ≥ 4.)