Determine whether f(x) = 3x + 1 and g(x) = (x-1) / 3 are inverses functions. Group of answer choices There are not inverses since both composition equal x. There are inverses since both composition equal x. There are inverses since both composition equal x + 1. There are not inverses since (f (g(x)) = x + 1

They are inverses since both composition equal x.

Step-by-step explanation:

Given the functions, f(x) = 3x + 1 and g(x) = (x-1) / 3, to check if they are inverses functions, we are to find the inverse of one of the function and check if it will give us the other function.

Let's look for the inverse of f(x).

Given f(x) = 3x+1

Let y = f(x) so that y = 3x+1

Replace y with x

x = 3y+1

Make y the subject of the formula of the resulting equation;

3y = x-1

y = (x-1)/3

The new function of x will be the inverse of f(x)

Hence f^-1(x) = (x-1)/3 = g(x)

Another way to check is to find their composition. Let's find f(g(x) and g(f(x)

F(g(x)) = f((x-1)/3)

Replace x with (x-1)/3 in f(x)

F(g(x)) = 3[(x-1)/3]+1

F(g(x)) = x-1+1

F(g(x)) = x

Similarly for g(f(x));

g(f(x)) = g(3x+1)

Replace x in g(x) with 3x+1

g(3x+1) = (3x+1-1)/3

g(3x+1) = 3x/3

g(3x+1) = x.

Since g(f(x)) = f(g(x)) = x, hence f(x) and g(x) are Inverses functions

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

d≈7.07in

step-by-step explanation: