Question

Given that f(x) = x + 3 and g(x) = x², answer the following questions:

i. Evaluate g(f(2)).
ii. Find g(f(x)).

a. g(f(2)) = 25, g(f(x)) = (x + 3)²
b. g(f(2)) = 25, g(f(x)) = x² + 6x + 9
c. g(f(2)) = 36, g(f(x)) = (x + 3)²
d. g(f(2)) = 36, g(f(x)) = x² + 3x + 6

Answer 1

To evaluate g(f(2)), substitute the value of f(2) into g(x). To find g(f(x)), substitute g(x) into f(x) and simplify.

Step-by-step explanation:

To evaluate g(f(2)), we first substitute the value of f(2) into the function g(x). Since f(x) = x + 3, we have f(2) = 2 + 3 = 5. Therefore, g(f(2)) = g(5).

Next, we substitute the value of g(f(x)) into the function f(x). Since g(x) = x², we have g(f(x)) = (x + 3)², as f(x) = x + 3.

So, the correct answers are:

i. g(f(2)) = g(5) = 5² = 25

ii. g(f(x)) = (x + 3)²