The square root function \( k(x) = \sqrt{5} x \) can be related to a quadratic function through squaring. To find the quadratic function related to \( k(x) \), we can express \( x \) in terms of \( k(x) \):
\[ k(x) = \sqrt{5} x \implies x = \frac{k(x)}{\sqrt{5}} \]
Now, squaring both sides gives us:
\[ x^2 = \left(\frac{k(x)}{\sqrt{5}}\right)^2 = \frac{k(x)^2}{5} \]
Thus, multiplying both sides by 5 yields:
\[ 5x^2 = k(x)^2 \]
This means that:
\[ m(x) = 5x^2 \]
From the options provided, we can see that:
- \( m(x) = 5x^2 \)
This matches one of the response options:
- m(x) = 5x²
So, the correct answer is:
m(x) = 5x².
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