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Magazine Problem 16
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. $$f(x)=\frac{x}{1-3 x}$$
Problem 17
Use the given pair of functions to find and simplify expressions for the following functions and state the domain of each using interval notation. $$\bullet (g \circ f)(x)$$ $$\bullet (f \circ g)(x)$$ $$\bullet (f \circ f)(x)$$ $$f(x)=|x+1|, g(x)=\sqrt{x}$$
Problem 17
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. $$f(x)=\frac{2 x-1}{3 x+4}$$
Problem 17
Solve the equation or inequality. $$x+1=\sqrt{3 x+7}$$
Problem 18
Use the given pair of functions to find and simplify expressions for the following functions and state the domain of each using interval notation. $$\bullet (g \circ f)(x)$$ $$\bullet (f \circ g)(x)$$ $$\bullet (f \circ f)(x)$$ $$f(x)=3-x^{2}, g(x)=\sqrt{x+1}$$
Problem 18
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. $$f(x)=\frac{4 x+2}{3 x-6}$$
Problem 18
Solve the equation or inequality. $$2 x+1=\sqrt{3-3 x}$$
Problem 19
Use the given pair of functions to find and simplify expressions for the following functions and state the domain of each using interval notation. $$\bullet (g \circ f)(x)$$ $$\bullet (f \circ g)(x)$$ $$\bullet (f \circ f)(x)$$ $$f(x)=|x|, g(x)=\sqrt{4-x}$$
Problem 19
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. $$f(x)=\frac{-3 x-2}{x+3}$$
Problem 19
Solve the equation or inequality. $$x+\sqrt{3 x+10}=-2$$
