91Ó°ÊÓ

Show that the given function is one-to-one and find its inverse. Check your answers algebraically and graphically. Verify that the range of \(f\) is the domain of \(f^{-1}\) and vice-versa. $$f(x)=\frac{x-2}{2 x-1}$$

Use the given pair of functions to find and simplify expressions for the following functions and state the domain of each using interval notation. $$\bullet (g \circ f)(x)$$ $$\bullet (f \circ g)(x)$$ $$\bullet (f \circ f)(x)$$ $$f(x)=x^{2}-x-1, g(x)=\sqrt{x-5}$$

Solve the equation or inequality. $$3 x+\sqrt{6-9 x}=2$$

Use the given pair of functions to find and simplify expressions for the following functions and state the domain of each using interval notation. $$\bullet (g \circ f)(x)$$ $$\bullet (f \circ g)(x)$$ $$\bullet (f \circ f)(x)$$ $$f(x)=3 x-1, g(x)=\frac{1}{x+3}$$

With help from your classmates, find the inverses of the functions in Exercises \(21-24\). $$f(x)=a x+b, a \neq 0$$

Solve the equation or inequality. $$2 x-1=\sqrt{x+3}$$

Solve the equation or inequality. $$x^{\frac{3}{2}}=8$$

With help from your classmates, find the inverses of the functions in Exercises \(21-24\). $$f(x)=a \sqrt{x-h}+k, a \neq 0, x \geq h$$

Solve the equation or inequality. $$x^{\frac{2}{3}}=4$$

Use the given pair of functions to find and simplify expressions for the following functions and state the domain of each using interval notation. $$\bullet (g \circ f)(x)$$ $$\bullet (f \circ g)(x)$$ $$\bullet (f \circ f)(x)$$ $$f(x)=\frac{x}{2 x+1}, g(x)=\frac{2 x+1}{x}$$