Guse the counting principle to determine the number of elements in the sample space. the possible ways to complete a multiple-choice test consisting of 20 questions, with each question having four possible answers (a, b, c, or d).

Step-by-step explanation:

Total number of questions = 20

Possible options for each question = 4

Sample space contains the total number of possible outcomes.

For every question there are 4 possible ways to select an answer. This holds true for all 20 questions. Selecting an answer for a question is independent of other questions/answers,

According to the counting principle, the total number of possible outcomes will be the product of the number of possible outcomes of individual events. Possible outcomes for each of the 20 questions is 4. This means we have to multiply 4 twenty times to find the total number of possible outcomes.

So, the number of elements in the sample space would be:

asnwer is (g o h o f)(x) = 2x - 6/x + 7

step-by-step explanation:

given,

f(x) = x - 3/x

g(x) = x + 3

h(x) = 2x + 1

we need to find : (g o h o f)(x)

we can write (g o h o f)(x) = g[ h{ f(x) } ]

so first we find h{f(x)}

h{f(x)} = f(x) + 3 = (x - 3/x) + 3

h{f(x)} = x - 3/x + 3

now we find g[ h{ f(x) } ].

g[ h{ f(x) } ] = g(x - 3/x + 3)       {plug h{f(x)} = x - 3/x + 3 in g[h{f(x)}] }

g(x - 3/x + 3) = 2 (x - 3/x + 3) + 1

                    = 2x - 6/x + 6 + 1

                    = 2x - 6/x + 7

hence we get (g o h o f)(x) = 2x - 6/x + 7