Explanation: In order to prove that one function is the inverse of the other, all you have to do is substitute in the main function with the inverse one and solve. If the result is x, then it is verified that one function is the inverse of the other. Now for the given functions we have: <span>f(x) =5x-25 </span><span>g(x) = (1/5)x+5 We want to prove that g(x) is the inverse of f(x). Substitute in the above formula and compute the result as follows: f(g(x)) = 5(</span>(1/5)x+5) - 25 = x + 25 - 25 = x The final result is "x", therefore, it is verified that g(x) is the inverse of f(x)
The volume of a sphere, V = (4/3)(PI)(R^3)
Let k = (4/3)(PI)
Therefore, V = k (R^3)
Let R’ = new radius = 2R
V’ =k (R’^3)
= k (2R)^3
= 8 k R^3
= 8 V
The volume would be eight time the original volume.
