Answer: choice A) -1
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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).