91Ó°ÊÓ

Write \(p(x)=1 / \sqrt{x^{2}+1}\) as a composite of three functions in two different ways.

In Problems 11-18, use a calculator to approximate each value. $$ \cos (\operatorname{arcsec} 3.212) $$

In Problems 1-30, plot the graph of each equation. Begin by checking for symmetries and be sure to find all \(x\) - and \(y\)-intercepts. $$ x^{2}-y^{2}=4 $$

In Problems \(11-16\), find the equation of the circle satisfying the given conditions. Center \((2,-1)\), goes through \((5,3)\)

Verify the following are identities. (a) \(\frac{\sin u}{\csc u}+\frac{\cos u}{\sec u}=1\) (b) \(\left(1-\cos ^{2} x\right)\left(1+\cot ^{2} x\right)=1\) (c) \(\sin t(\csc t-\sin t)=\cos ^{2} t\) (d) \(\frac{1-\csc ^{2} t}{\csc ^{2} t}=\frac{-1}{\sec ^{2} t}\)

Simplify as much as possible. Be sure to remove all parentheses and reduce all fractions. \(1-\frac{1}{1+\frac{1}{2}}\)

In Problems \(11-16\), find the inverse of the given function \(f\) and verify that \(f\left(f^{-1}(x)\right)=x\) for all \(x\) in the domain of \(f^{-1}\), and \(f^{-1}(f(x))=x\) for all \(x\) in the domain of \(f\). $$ f(x)=\frac{10^{x}}{1+10^{x}} $$

Simplify as much as possible. Be sure to remove all parentheses and reduce all fractions. \(2+\frac{3}{1+\frac{5}{2}}\)

Express the solution set of the given inequality in interval notation and sketch its graph. $$ 4 x^{2}-5 x-6<0 $$

Write \(p(x)=1 / \sqrt{x^{2}+1}\) as a composite of four functions.