Consider the following two statements and choose the correct answer. (i) If f(x)f(x) is continuous at x=ax=a, then f(x)f(x) is differentiable at x=ax=a.

(ii) For every fixed constant cc, the (natural) domain of f(x)=3x+ln(x−c)f(x)=3x+ln⁡(x−c) is [c,∞)[c,∞).

For problems 7–10, state a reasonable domain for the problem statement, find the inverse functionf –1(x), and identify the independent and dependent quantities of the inverse. gary is jogging. the total distance he has traveled, in miles, can be estimated using the functionf(x) = 9x, where x is his jogging time in hours. camryn sells computers. she earns commission for her computer sales plus a fixed wage for each day she works. her daily earnings, in dollars, can be estimated using the functionf(x) = 0.15x + 50, where x represents her computer sales in dollars. the distance a motorboat travels, in meters, can be estimated using the equation f(x) = 1.9x2, wherexisthetimeinseconds,for0≤x≤10. a rock band is selling tickets to a concert at a theater. the band earns money for each ticket sold, but has to pay some of the earnings to the theater. the total money earned by the band can be estimated using the function f(x) = 7.5x – 300, where x is the number of tickets sold.