Solving Rational and Fractional Functions

SAT Subject Test in Math II · Learn by Concept

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SAT Subject Test in Math II › Solving Rational and Fractional Functions

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If $f(x) = 2\sqrt{x}-\sqrt{x-3}$ , what is the value of ?

$2i\sqrt3 -i\sqrt6$

CORRECT

$i\sqrt6$

$-2i\sqrt3$

Substitute the value of negative three as .

$f(-3) = 2\sqrt{-3}-\sqrt{(-3)-3}$

$2\sqrt{-3}-\sqrt{-6} = 2\sqrt{-1}\cdot \sqrt{3} - \sqrt{-1}\cdot \sqrt{6}$

The terms will be imaginary. We can factor out an $i = \sqrt{-1}$ out of the right side. Replace them with .

The answer is: $2i\sqrt3 -i\sqrt6$