91Ó°ÊÓ

Let \(f=\\{(2,6),(3,8),(4,5)\\}\) and \(g(x)=3 x+5 .\) Find the following. $$x, \text { if } g(x)=26$$

Let \(f(x)=x-2, g(x)=\sqrt{x},\) and \(h(x)=\frac{1}{x} .\) Find an equation defining each function and state the domain of the function. $$h \circ f \circ g$$

Weight of a Can The weight of a can of baked beans varies jointly with the height and the square of the diameter. If a 4 -in.-high can with a 3 -in. radius weighs 14.5 oz, then what is the weight of a 5 -in.-high can with a diameter of 6 in.?

Determine algebraically whether the function is even, odd, or neither. Discuss the symmetry of each function. $$f(x)=x^{4}$$

Find the inverse of each function and graph both \(f\) and \(f^{-1}\) on the same coordinate plane. $$f(x)=x^{2}-4 \text { for } x \geq 0$$

Find the inverse of each function and graph both \(f\) and \(f^{-1}\) on the same coordinate plane. $$f(x)=1-x^{2} \text { for } x \geq 0$$

Let \(f=\\{(2,6),(3,8),(4,5)\\}\) and \(g(x)=3 x+5 .\) Find the following. $$x, \text { if } g(x)=4$$

Make a table listing ordered pairs for each function. Then sketch the graph and state the domain and range. Identify any intervals on which \(f\) is increasing, decreasing, or constant. $$f(x)=\frac{2 x}{|x|}$$

Determine algebraically whether the function is even, odd, or neither. Discuss the symmetry of each function. $$f(x)=x^{4}-2 x^{2}$$

Nitrogen Gas Shock Absorber The volume of gas in a nitrogen gas shock absorber varies directly with the temperature of the gas and inversely with the amount of weight on the piston. If the volume is 10 in. \(^{3}\) at \(80^{\circ} \mathrm{F}\) with a weight of 600 lb, then what is the volume at \(90^{\circ} \mathrm{F}\) with a weight of \(800 \mathrm{lb} ?\)