91Ó°ÊÓ

In Problems \(1-10,\) find the functions \(f+g, f-g, f g\), and \(f / g\), and give their domains. $$ f(x)=x, \quad g(x)=\sqrt{x-1} $$

In Problems \(1-4\), find the indicated values of the given piecewise-defined function \(f\). $$ f(x)=\left\\{\begin{array}{ll} x^{2}+2 x, & x \geq 1 \\ -x^{3}, & x<1 ; \end{array} \quad f(1), f(0), f(-2), f(\sqrt{2})\right. $$

Find two functions defined implicitly by the given equation. Graph each function. $$ x+y=5 $$

Proceed as in Example 1 and translate the words into an appropriate function. Give the domain of the function. The sum of two nonnegative numbers is 1 . Express the sum of the square of one and twice the square of the other as a function of one of the numbers.

Find the slope of the line through the given points. Graph the line through the points. (1,4),(6,-2)

In Problems \(1-4\), find the indicated values of the given piecewise-defined function \(f\). $$ f(x)=\left\\{\begin{array}{ll} x^{2}+2 x, & x \geq 1 \\ -x^{3}, & x<1 ; \end{array} \quad f(1), f(0), f(-2), f(\sqrt{2})\right. $$

Find two functions defined implicitly by the given equation. Graph each function. $$ (y-1)^{2}=4(x+2) $$

Determine whether the given function \(y=f(x)\) is even, odd, or neither even nor odd. Do not graph. $$ f(x)=x^{5}+x^{3}+x $$

In Problems \(1-10,\) find the functions \(f+g, f-g, f g\), and \(f / g\), and give their domains. $$ f(x)=x-2, \quad g(x)=\frac{1}{x+8} $$

Find the indicated function values. If \(f(x)=\sqrt{2 x+4} ; \quad f\left(-\frac{1}{2}\right), f\left(\frac{1}{2}\right), f\left(\frac{5}{2}\right),\) and \(f(4)\)