Identify a domain on which the function f(x) = x2 + 7 is one-to-one. Select the appropriate domain(s). ID = { x: -7 = The volume V of a cone that has height equal to its radius r is given by V(r) = 1rr3. Find the inverse of V(r), expressing r as a function of V. (Express numbers in exact form. Use Symbolic notation and fractions where needed.) r= : The surface area S of a sphere of radius r is given by S(r) = 47:12. Explain why, in the given context, S(r) has an inverse function. Identify the correct explanation. O S(r) is decreasing on its domain and therefore is one-toone. O S(r) is increasing on its domain and therefore is one-toone. O S(r) is linear and must have an inverse. O S(r) is a polynomial and all polynomials are one-toone for all real numbers. 0 S(r) is both increasing and decreasing on its domain. Find the inverse of S(r), expressing r as a function of S. (Express numbers in exact form. Use symbolic notation and fractions where needed.) I n correct Using interval notation, determine the largest domain over which the given function is one-to-one. Then, provide the equation for the inverse of the function that is restricted to that domain. If two equally large domains exist over which the given function is one-to-one, you may use either domain. However, be certain that the equation for the inverse function you submit is appropriate for the particular domain you choose. 1 3x+4 f(x) = I n co rrect Using interval notation, determine the largest domain over which the given function is one-to-one. Then, provide the equation for the inverse of the function that is restricted to that domain. If two equally large domains exist over which the given function is one-to-one, you may use either domain. However, be certain that the equation for the inverse function you submit is appropriate for the particular domain you choose. f(x) = 32x5 dorm E f'1 =