91Ó°ÊÓ

The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\). $$f(x)=2 x$$

For each pair of functions, \(f\) and \(g\) determine the domain of \(f+g\) $$f(x)=\frac{8 x}{x-2}, g(x)=\frac{6}{2-x}$$

Express each interval in set-builder notation and graph the interval on a number line. $$(2, \infty)$$

Express each interval in set-builder notation and graph the interval on a number line. $$(3, \infty)$$

For each pair of functions, \(f\) and \(g\) determine the domain of \(f+g\) $$f(x)=\frac{9 x}{x-4}, g(x)=\frac{7}{4-x}$$

The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\). $$f(x)=4 x$$

Find \(f(-x)-f(x)\) for the given function \(f\) Then simplify the expression. $$f(x)=x^{3}+x-5$$

Express each interval in set-builder notation and graph the interval on a number line. $$[-3, \infty)$$

For each pair of functions, \(f\) and \(g\) determine the domain of \(f+g\) \(f(x)=x^{2}, g(x)=x^{3}\)

The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\). $$f(x)=2 x+3$$