Question

Find g(f(2)).

g(n) = 3n + 2
f(n) = 2n² + 5

a) 41
b) 133
c) 21
d) 8

Answer 1

g(f(2)) = 41, option a).

Step-by-step explanation:

1. Find f(2)

f(n) = 2n² + 5

f(2) = 2(2)² + 5

f(2) = 13

2. Find g(13)

g(n) = 3n + 2

g(13) = 3(13) + 2

g(13) = 41

Therefore g(f(2)) = 41, option a).

Answer 2

After evaluating the inner function f(2), which yields 13, and then substituting this result into the outer function g(n), the final result for g(f(2)) is determined to be 41.

Step-by-step explanation:

To solve for g(f(2)), you must first evaluate the inner function f(2) and then use this result to evaluate the outer function, g, at that value.

The function f(n) is defined as f(n) = 2n² + 5. To find f(2), substitute 2 for n:

f(2) = 2(2)² + 5
= 2(4) + 5
= 8 + 5
= 13

Now that you have f(2) = 13, use this result to evaluate g(f(2)), which means substituting 13 into the function g(n), given by g(n) = 3n + 2.

g(f(2)) = g(13)
= 3(13) + 2
= 39 + 2
= 41

Therefore, g(f(2)) is 41.