Question

Use the pair of functions to find f(g(0)) and g(f(0)).

a. f(g(0))=27, g(f(0))=2
b. f(g(0))=3, g(f(0))=30
c. f(g(0))=30, g(f(0))=3
d. f(g(0))=2, g(f(0))=27

Answer 1

a. f(g(0)) = 27, g(f(0)) = 2

b. f(g(0)) = 3, g(f(0)) = 30

c. f(g(0)) = 30, g(f(0)) = 3

d. f(g(0)) = 2, g(f(0)) = 27

Step-by-step explanation:

a) Here, we are given that f(g(0)) = 27 and g(f(0)) = 2. To find the values of f and g, we can use the following steps:

i) Firstly, let's find the value of g when applied to f(0). This can be done by substituting f(0) in the expression of g. Therefore, g(f(0)) = g(0) = 2.

ii) Now, let's find the value of f when applied to g(0). This can be done by substituting g(0) in the expression of f. Therefore, f(g(0)) = f(2) = 27.

b) Here, we are given that f(g(0)) = 3 and g(f(0)) = 30. To find the values of f and g, we can use the following steps:

i) Firstly, let's find the value of g when applied to f(0). This can be done by substituting f(0) in the expression of g. Therefore, g(f(0)) = g(0) = 30.

ii) Now, let's find the value of f when applied to g(0). This can be done by substituting g(0) in the expression of f. Therefore, f(g(0)) = f(30) = 3.

c) Here, we are given that f(g(0)) = 30 and g(f(0)) = 3. To find the values of f and g, we can use the following steps:

i) Firstly, let's find the value of g when applied to f(0). This can be done by substituting f(0) in the expression of g. Therefore, g(f(0)) = g(3) = 3.

ii) Now, let's find the value of f when applied to g(0). This can be done by substituting g(0) in the expression of f. Therefore, f(g(0)) = f(3) = 30.

d) Here, we are given that f(g(0)) = 2 and g(f(0)) = 27. To find the values of f and g, we can use the following steps:

i) Firstly, let's find the value of g when applied to f(0). This can be done by substituting f(0) in the expression of g. Therefore, g(f(0)) = g(-1) (as we know that when a function is not defined for a particular input value (here -1), then it is denoted as -1). Since -1 is not defined in this case, we cannot calculate this value directly from given information. Hence this is an invalid pair of functions as it does not satisfy all conditions for function composition (i.e., domain and range conditions).