Question

Given two functions: f(x) = x² and g(x) = x + 3, find the following:

a) Find f(g(5))
b) Find g(f(5))

A) a) f(g(5)) = 64; b) g(f(5)) = 28
B) a) f(g(5)) = 28; b) g(f(5)) = 64
C) a) f(g(5)) = 64; b) g(f(5)) = 64
D) a) f(g(5)) = 28; b) g(f(5)) = 28

Answer 1

The function compositions are calculated by substituting the inner function result into the outer function. The calculated answers are f(g(5)) = 64 and g(f(5)) = 28.

Step-by-step explanation:

When you're asked to find f(g(5)) and g(f(5)) given two functions, this is a question of function composition. You must evaluate the inner function first and then use that result as the input for the outer function.

To find f(g(5)):

1. Evaluate g(5), which is 5 + 3 = 8.
2. Next, plug this result into f(x), so f(g(5)) becomes f(8).
3. Finally, calculate f(8), which is 82 = 64.

So, f(g(5)) = 64.

To find g(f(5)):

1. Evaluate f(5), which yields 52 = 25.
2. Next, plug this result into g(x), giving us g(f(5)), which is g(25).
3. Last, compute g(25), which is 25 + 3 = 28.

Therefore, g(f(5)) = 28.

The correct answer is a) f(g(5)) = 64; b) g(f(5)) = 28.