91Ó°ÊÓ

Let \(f(x)=x^{2}-6 x-4 .\) Find \(f(3-\sqrt{13})\)

In Exercises \(113-116\), use the distributive property or the FOIL method to perform each multiplication. $$x^{\frac{1}{3}}\left(x^{\frac{1}{3}}-x^{\frac{2}{5}}\right)$$

In Exercises \(113-116\), use the distributive property or the FOIL method to perform each multiplication. $$x^{-\frac{1}{4}}\left(x^{\frac{9}{4}}-x^{\frac{1}{2}}\right)$$

Let \(f(x)=x^{2}+4 x-2 .\) Find \(f(-2+\sqrt{6})\)

In Exercises \(111-114\), simplify each evaluation to the form \(a+b i\) $$\text { Let } f(x)=\frac{x^{2}+11}{3-x} . \text { Find } f(4 i)$$

In Exercises \(113-116\), use the distributive property or the FOIL method to perform each multiplication. $$\left(x^{\frac{1}{2}}-3\right)\left(x^{\frac{1}{2}}+5\right)$$

Let \(f(x)=\sqrt{9+x} .\) Find \(f(3 \sqrt{5}) \cdot f(-3 \sqrt{5})\)

Complex numbers are used in electronics to describe the current in an electric circuit. Ohm's law relates the current in a circuit, \(I,\) in amperes, the voltage of the circuit, \(E,\) in volts, and the resistance of the circuit, \(R,\) in ohms, by the formula \(E=I R .\) Use this formula to solve Exercises \(115-116\) Find \(E,\) the voltage of a circuit, if \(I=(4-5 i)\) amperes and \(R=(3+7 i)\) ohms.

If a number is tripled, what happens to its square root?

Use a graphing utility to graph \(y_{1}=\sqrt{x}, y_{2}=\sqrt{x+4}\) and \(y_{3}=\sqrt{x-3}\) in the same \([-5,10,1]\) by \([0,6,1]\) viewing rectangle. Describe one similarity and one difference that you observe among the graphs. Use the word shift in your response.