91Ó°ÊÓ

Finding Equations for Transformations A function \(f\) is given, and the indicated transformations are applied to its graph (in the given order). Write an equation for the final transformed graph. \(f(x)=\sqrt[3]{x} ;\) shift 1 unit to the right

Find the domain of the function. $$f(x)=\frac{x+2}{x^{2}-1}$$

Find the functions \(f \circ g\) \(g \circ f, f \circ f,\) and \(g \circ g\) and their domains. $$f(x)=\frac{x}{x+1}, \quad g(x)=\frac{1}{x}$$

Determine whether the equation defines \(y\) as a function of \(x .\) (See Example 9.) $$3 x-5 y=7$$

Find the inverse function of \(f.\) $$f(x)=\frac{2 x+5}{x-7}$$

Finding Equations for Transformations A function \(f\) is given, and the indicated transformations are applied to its graph (in the given order). Write an equation for the final transformed graph. \(f(x)=|x| ;\) shift 2 units to the left and shift downward 5 units

Finding Equations for Transformations A function \(f\) is given, and the indicated transformations are applied to its graph (in the given order). Write an equation for the final transformed graph. \(f(x)=|x| ;\) reflect in the \(x\) -axis, shift 4 units to the right, and shift upward 3 units.

Find the domain of the function. $$f(x)=\frac{x^{4}}{x^{2}+x-6}$$

Find the functions \(f \circ g\) \(g \circ f, f \circ f,\) and \(g \circ g\) and their domains. $$f(x)=\frac{2}{x}, \quad g(x)=\frac{x}{x+2}$$

Find the inverse function of \(f.\) $$f(x)=\frac{4 x-2}{3 x+1}$$