The function \( f(x)=\frac{4 x+5}{x+4} \) is one-to-one. (a) Find its inverse and check your answer. (b) Find the domain and the range of \( f \) and \( f^{-1} \). (a) \( f^{-1}(x)=\frac{5-4 x}{x-4} \) (Simplify your answer.) (b) Find the domain of \( f \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice (Type integers or fractihs. Use a comma to separate answers as needed.) B. The domain is \( \{x \mid x \leq \). (Type integers or fractions. Use a comma to separate answers as needed.) C. The domain is \( \{x \mid x \geq\} \). (Type integers or fractions. Use a comma to separate answers as needed.) D. The domain is the set of all real numbers.

Simplify. \[ \frac{3 x^{2}-6 x}{4 x^{2}-8 x} \]

a) \( 7 x+(3 x-5)=6 x-9 \)

Simplify. \[ \frac{10 y^{2}-25 y}{5 y^{2}-15 y} \]

Find the range of the quadratic function, \[ y=-3 x^{2}-12 x-15 \] Write your answer as an inequality using \( x \) or \( y \) as appropriate, Or, you may instead click on "Empty set" or "All reals" as the answer, प<ロ \( \square>\square \)

10. Matador Wireless offers a data plan that charges \( \$ 10.00 \) a month for access, with no additional charge if usage is at or below 75 MB . If a customer exceeds 75 MB of data they are also charged 10 cents for each MB above 75 . If a customer exceeds 125 MB of data, they are charged 40 cents for each MB above 125 . a. What is the monthly cost to store 125 MB of data? b. Write a formula for the piecewise function of the cost function for storing \( x \mathrm{MB} \) of data a month. Fill in the boxes for the piecewise definition for the cost \( C(x) \) of storing \( x \) MB of data a month. \[ C(x)=\left\{\begin{array}{cc}10 & \text { if } 0 \leq x \leq 75 \\ 10+0.10(x-75) & \text { if } 75<x \leq 125 \\ 10+0.10(50)+0.40(x-125) & \text { if } x>125\end{array}\right. \]