Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of nonnegative integers to the set of integers. If f is well defined, find a formula for f (n) when n is a nonnegative integer and prove that your formula is valid. a) f (0) = 0, f (n) = 2f (n â 2) for n ⥠1 b) f (0) = 1, f (n) = f (n â 1) â 1 for n ⥠1 c) f (0) = 2, f (1) = 3, f (n) = f (n â 1) â 1 for n ⥠2 d) f (0) = 1, f (1) = 2, f (n) = 2f (n â 2) for n ⥠2 e) f (0) = 1, f (n) = 3f (n â 1) if n is odd and n ⥠1 and f (n) = 9f (n â 2) if n is even and n ⥠2.

Use composition to determine if (x) or h(x) is the inverse of f(x) for the limited domain x2-1.

For f(x) = 3x+1 and g(x) = x2 - 6, find (g/f)(x)

Farmers know that driving heavy equipment on wet soil compresses the soil and injures future crops. here are data on the "penetrability" of the same type of soil at two levels of compression. penetrability is a measure of how much resistance plant roots will meet when they try to grow through the soil. compressed soil 2.85 2.66 3 2.82 2.76 2.81 2.78 3.08 2.94 2.86 3.08 2.82 2.78 2.98 3.00 2.78 2.96 2.90 3.18 3.16 intermediate soil 3.17 3.37 3.1 3.40 3.38 3.14 3.18 3.26 2.96 3.02 3.54 3.36 3.18 3.12 3.86 2.92 3.46 3.44 3.62 4.26 use the data, omitting the high outlier, to give a 95% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil. compute degrees of freedom using the conservative method. interval: to