Question

Which of the following correctly identifies the quadratic function that is related to the square root function k(x)=5x−−√
?(1 point)

m(x)=125x2


m(x)=25x2


m(x)=15x2


m(x)=5x2

Answer 1

I need one quick clarification: do you mean k(x) = √(5x) (square root of 5x) or k(x) = 5√x (5 times √x)? And by "related" do you mean the inverse (reflection across y = x) or something else (e.g. square the function)?

Common cases:
- If k(x) = √(5x) and you want the inverse, swap and solve: y = √(5x) ⇒ x = y^2/5 ⇒ inverse m(x) = (1/5)x^2.
- If k(x) = 5√x and you want the inverse: y = 5√x ⇒ x = y^2/25 ⇒ inverse m(x) = (1/25)x^2.
- If by "related" you mean square the function, (k(x))^2 = 5x (not quadratic in x).

None of the given choices (125x^2, 25x^2, 15x^2, 5x^2) match the inverse in either interpretation, so with the usual meaning (inverse) the correct answer is not listed. Tell me which meaning you intended and I’ll pick the right choice.