91Ó°ÊÓ

Determine whether the graphs of the following equations and fimctions are symmetric about the \(x\)-axis, the \(y\) -axis, or the origin. Check your work by graphing. $$f(x)=x|x|$$

Find all the inverses associated with the following functions, and state their domains. \(f(x)=x^{2}-2 x+6(\text {Hint:}\) Complete the square first.)

Use a right triangle to simplify the given expressions. Assume \(x>0 .\) $$\cot \left(\tan ^{-1} 2 x\right)$$

Determine whether the graphs of the following equations and fimctions are symmetric about the \(x\)-axis, the \(y\) -axis, or the origin. Check your work by graphing. $$|x|+|y|=1$$

Find all the inverses associated with the following functions, and state their domains. $$f(x)=(x+1)^{3}$$

Assume \(f\) is an even function, \(g\) is an odd function, and both are defined at 0 Use the (incomplete) table to evaluate the given compositions. $$\begin{array}{lrrrr}\hline x & 1 & 2 & 3 & 4 \\\f(x) & 2 & -1 & 3 & -4 \\\g(x) & -3 & -1 & -4 & -2 \\\\\hline\end{array}$$ a. \(f(g(-1))\) b. \(g(f(-4))\) c. \(f(g(-3))\) d. \(f(g(-2))\) e. \(g(g(-1))\) f. \(f(g(0)-1)\) g. \(f(g(g(-2)))\) h. \(g(f(f(-4)))\) i. \(g(g(g(-1)))\)

Use a right triangle to simplify the given expressions. Assume \(x>0 .\) $$\cos \left(\tan ^{-1}\left(\frac{x}{\sqrt{9-x^{2}}}\right)\right.$$

Find all the inverses associated with the following functions, and state their domains. $$f(x)=(x-4)^{2}$$

Find all the inverses associated with the following functions, and state their domains. $$f(x)=2 /\left(x^{2}+2\right)$$

Show that the graph of \(f(x)=10+\sqrt{-x^{2}+10 x-9}\) is the upper half of a circle. Then determine the domain and range of the function.