If f(x) = x² − 3 and f(a) = 13, where a > 0, what is a?

Correct answer: 4

The governing concept is using the definition of a function to form and solve an equation. Substituting a into f(x) = x² − 3 gives f(a) = a² − 3. Because f(a) = 13, we set a² − 3 = 13. Adding 3 to both sides gives a² = 16. Taking square roots yields a = 4 or a = −4. The additional condition a > 0 is decisive, so the acceptable value is a = 4. Hence option A is correct. Option B is the squared value a², not the required input. Option C is the other algebraic root but is excluded because it is negative. Option D fails the original condition, since 5² − 3 = 22 rather than 13. Both substitution and the sign condition must be used.