91Ó°ÊÓ

A function \(f\) is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph. \(f(x)=x^{2} ;\) shift 2 units to the left and reflect in the \(x\) -axis

Find the inverse function of \(f .\) $$f(x)=x^{2}+x, \quad x \geq-\frac{1}{2}$$

Find the domain of the function. $$f(x)=\sqrt[4]{x+9}$$

Find the inverse function of \(f .\) $$f(x)=4-x^{2}, \quad x \geq 0$$

Find the domain of the function. $$f(t)=\sqrt[3]{t}-1$$

A function \(f\) is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph. \(f(x)=x^{2} ;\) stretch vertically by a factor of \(2,\) shift downward 2 units, and shift 3 units to the right

A highway engineer wants to estimate the maximum number of cars that can safely travel a particular highway at a given speed. She assumes that each car is \(17 \mathrm{ft}\) long, travels at a speed \(s,\) and follows the car in front of it at the "safe following distance" for that speed. She finds that the number \(N\) of cars that can pass a given point per minute is modeled by the function $$N(s)=\frac{88 s}{17+17\left(\frac{s}{20}\right)^{2}}$$ At what speed can the greatest number of cars travel the highway safely?

A function \(f\) is given, and the indicated transformations are applied to its graph (in the given order). Write the equation for the final transformed graph. \(f(x)=|x| ;\) shrink vertically by a factor of \(\frac{1}{2},\) shift to the left 1 unit, and shift upward 3 units

Find the domain of the function. $$g(x)=\sqrt{7}-3 x$$

Express the function in the form \(f \circ g\) $$H(x)=\sqrt{1+\sqrt{x}}$$