If f(x) = 2x-1, find the zero of f^-1(x) a. -1 b. 1/2 c. 1 and explain!

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).

the co-ordinates of the transformed rectangle are:

d. (0, 0), (0, 3), (-3, 3), (-3, 0)

step-by-step explanation:

from the columns of the given matrix, the co-ordinates of the rectangle before transformation are:

(0, 0), (0, 3), (3, 3), (3, 0)

r =

transformed matrix can be obtained by multiplying the given matrix by r:

columns of the transformed matrix are:

0   0   -3   -3

0   3     3     0

from the columns of the resulted matrix, we can see that the vertices of the transformed triangle are:

(0, 0), (0, 3), (-3, 3), (-3, 0)