91Ó°ÊÓ

For each function. \(\bullet\) Find its domain. \(\bullet\) Create a sign diagram. \(\bullet\) Use your calculator to help you sketch its graph and identify any vertical or horizontal asymptotes, 'unusual steepness' or cusps. $$f(x)=\sqrt{1-x^{2}}$$

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. $$f(x)=6 x-2$$

Use the given pair of functions to find the following values if they exist. $$\bullet (g \circ f)(0)$$ $$\bullet (f \circ g)(-1)$$ $$\bullet (f \circ f)(2)$$ $$\bullet (g \circ f)(-3)$$ $$\bullet (f \circ g)\left(\frac{1}{2}\right)$$ $$\bullet (f \circ f)(-2)$$ $$f(x)=x^{2}, g(x)=2 x+1$$

Use the given pair of functions to find the following values if they exist. $$\bullet (g \circ f)(0)$$ $$\bullet (f \circ g)(-1)$$ $$\bullet (f \circ f)(2)$$ $$\bullet (g \circ f)(-3)$$ $$\bullet (f \circ g)\left(\frac{1}{2}\right)$$ $$\bullet (f \circ f)(-2)$$ $$f(x)=4-x, g(x)=1-x^{2}$$

For each function. \(\bullet\) Find its domain. \(\bullet\) Create a sign diagram. \(\bullet\) Use your calculator to help you sketch its graph and identify any vertical or horizontal asymptotes, 'unusual steepness' or cusps. $$f(x)=\sqrt{x^{2}-1}$$

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. $$f(x)=42-x$$

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. $$f(x)=\frac{x-2}{3}+4$$

For each function. \(\bullet\) Find its domain. \(\bullet\) Create a sign diagram. \(\bullet\) Use your calculator to help you sketch its graph and identify any vertical or horizontal asymptotes, 'unusual steepness' or cusps. $$f(x)=x \sqrt{1-x^{2}}$$

Use the given pair of functions to find the following values if they exist. $$\bullet (g \circ f)(0)$$ $$\bullet (f \circ g)(-1)$$ $$\bullet (f \circ f)(2)$$ $$\bullet (g \circ f)(-3)$$ $$\bullet (f \circ g)\left(\frac{1}{2}\right)$$ $$\bullet (f \circ f)(-2)$$ $$f(x)=4-3 x, g(x)=|x|$$

Use the given pair of functions to find the following values if they exist. $$\bullet (g \circ f)(0)$$ $$\bullet (f \circ g)(-1)$$ $$\bullet (f \circ f)(2)$$ $$\bullet (g \circ f)(-3)$$ $$\bullet (f \circ g)\left(\frac{1}{2}\right)$$ $$\bullet (f \circ f)(-2)$$ $$f(x)=|x-1|, g(x)=x^{2}-5$$