Whats the last common multple of 2,5,6,9 and 9 is

"9 and 9?"  Did you possibly mean {2, 5, 6, 9}?

The least common multiple of a set of numbers is the smallest integer that can be divided evenly by all of the numbers.  In this case, when I saw the 9 and 5, I thought, "45!"  but 45 is not evenly divisible by 2 or 6.  

So, I tried 90.  90 is indeed divisible by {2, 5, 6, 9}, and is thus the LCM.

Look up and review "Least common multiple."

choice A) -1

I'm going to let g(x) be the inverse of f(x) to avoid using the clunky notation f^-1(x)

To find g(x), we need to do the following: first replace f(x) with y, then swap x and y, and finally solve for y

f(x) = 2x - 1

y = 2x - 1 replace f(x) with y

x = 2y - 1 swap x and y

x+1 = 2y

2y = x+1

y = (x+1)/2

g(x) = (x+1)/2

Now that we have the inverse function, we can find the root of this function. A root is when the output is 0. Replace g(x) with 0 and solve for x

g(x) = (x+1)/2

0 = (x+1)/2

2*0 = x+1

0 = x+1

x+1 = 0

x = -1

So plugging x = -1 into g(x) leads to g(x) = 0. This shows that x = -1 is a root of g(x).