91Ó°ÊÓ

An equation of the form \(|f(x)|=|g(x)|\) is given. (a) Solve the equation analytically and support the solution graphically. (b) Solve \(|f(x)|>|g(x)|\). (c) Solve \(|f(x)|<|g(x)|\). $$|0.40 x+2|=|0.60 x-5|$$

Use the analyric method of Example 3 to determine whether the graph of the given function is symmetric with respect to the \(y\) -axis, symmetric with respect to the origin, or neither. Use \(a\) calculator and the standand window to support your conclusion. $$f(x)=\sqrt{x^{2}}$$

Consider the function \(h\) as defined. Find functions \(f\) and \(g\) such that \((f \circ g)(x)=h(x)\). (There are several possible ways to do this.) $$h(x)=\sqrt{x^{2}-1}$$

An equation of the form \(|f(x)|=|g(x)|\) is given. (a) Solve the equation analytically and support the solution graphically. (b) Solve \(|f(x)|>|g(x)|\). (c) Solve \(|f(x)|<|g(x)|\). $$|3 x+10|=|-3 x-10|$$

An equation of the form \(|f(x)|=|g(x)|\) is given. (a) Solve the equation analytically and support the solution graphically. (b) Solve \(|f(x)|>|g(x)|\). (c) Solve \(|f(x)|<|g(x)|\). $$|5 x-6|=|-5 x+6|$$

Solve each equation graphically. $$|x+1|+|x-6|=11$$

Consider the function \(h\) as defined. Find functions \(f\) and \(g\) such that \((f \circ g)(x)=h(x)\). (There are several possible ways to do this.) $$h(x)=\sqrt{6 x}+12$$

Solve each equation graphically. $$|2 x+2|+|x+1|=9$$

Solve the following. Complete the following. (a) Write a function \(F\) that converts \(x\) miles to feet. (b) Write a function \(I\) that converts \(x\) feet to inches. (c) Write a formula for the composition \((I \circ F)(x)\) (d) Explain what \((I \circ F)(x)\) calculates.

Solve each equation graphically. $$|x|+|x-4|=8$$