## Solve Lesson 36 Page 59 Math 10 – Kite >

Topic

Which of the following statements is correct?

A. The solution set of the equation $$\sqrt {f\left( x \right)} = \sqrt {g\left( x \right)}$$ is the solution set of the equation $$f\left( x$$ right) = g\left( x \right)\)

B. The solution set of the equation $$\sqrt {f\left( x \right)} = \sqrt {g\left( x \right)}$$ is the solution set of the equation $${\left)[ {f\left( x \right)} \right]^2} = {\left[ {g\left( x \right)} \right]^2}$$

C. The solution set of the equation $$f\left( x \right) = g\left( x \right)$$ is the solution set of the equation $$\sqrt {f\left( x \right)} = \ sqrt {g\left( x \right)}$$

D. The solution set of the equation $$\sqrt {f\left( x \right)} = \sqrt {g\left( x \right)}$$ is the solution set of the equation $$f\left( x$$ right) = g\left( x \right)\) satisfying the inequality $$f\left( x \right) \ge 0$$ (or $$g\left( x \right) \ge 0$$ )

Solution method – See details

$$\sqrt {f\left( x \right)} = \sqrt {g\left( x \right)} \Leftrightarrow \left\{ \begin{array}{l}f(x) \ge 0\\ f\left( x \right) = g\left( x \right)\end{array} \right.$$or $$\left\{ \begin{array}{l}g(x) \ge 0\ \f\left( x \right) = g\left( x \right)\end{array} \right.$$

Detailed explanation

We have: $$\sqrt {f\left( x \right)} = \sqrt {g\left( x \right)} \Leftrightarrow \left\{ \begin{array}{l}f(x) \ge 0\\f\left( x \right) = g\left( x \right)\end{array} \right.$$

Thus the solution set of the equation $$\sqrt {f\left( x \right)} = \sqrt {g\left( x \right)}$$ is the set of solutions of the equation $$f\left( x$$ right) = g\left( x \right)\) satisfying the inequality $$f\left( x \right) \ge 0$$ (or $$g\left( x \right) \ge 0$$ )

Choose D.