# 10 and 21

For problem 10, we know that the descriminant must be equivalent to 0 in order for there to be one solution because a number + or - zero will only yield one answer. There for we set the descriminat of the problem to zero and solve for k.

b^2 - 4ac = 0
20^2 -4*3*k = 0
400- 12k =0
-12k = -400
k = 100/3

For problem 21 we are trying to find the inverse of the function. In order to do this we must call f(x) a variable y and re write the equation switching the x and the y variable. Then solve for the y variable, which will give you the inverse equation.

f(x) = log(2x - 1)
y = log(2x - 1)
x = log(2y - 1)
10^x = 2y - 1
(10^x +1)/2 = y