Question 1: If f(x) = 2x + 3 and g(x) = x - 4, calculate f(g(5)).

Answer: 7

Question 2: Given f(x) = x^2 and g(x) = 3x + 1, find the value of f(g(2)).

Answer: 49

Question 3: Calculate f(g(0)) where f(x) = 4 - x and g(x) = 2x + 5.

Answer: -1

Question 4: Construct the graph of y = f(g(x)) where f(x) = x + 2 and g(x) = 3x.

Answer: Student draws the graph showing y = 3x + 2.

Question 5: If f(x) = 5x - 1 and g(x) = x/2, what is f(g(8))?

Answer: 19

Question 6: A rectangle’s length is g(x) = 2x + 1, and its width is f(x) = 3x. Find the area when x = 4, i.e., calculate f(g(4)).

Answer: 45

Question 7: Describe step-by-step how to evaluate f(g(3)) if f(x) = x^2 + 1 and g(x) = 2x - 5.

Answer: Calculate g(3)=2*3-5=1, then f(1)=1^2+1=2.

Question 8: Find the value of f(g(x)) when f(x) = x - 3 and g(x) = 4x + 2, for x=6.

Answer: 24

Question 9: A garden design uses g(x) = x + 5 for the length and f(x) = 2x for the width. Find the total perimeter when x=7.

Answer: 54

Question 10: A student mistakenly calculates f(g(2)) by swapping the functions. Identify and explain the mistake.

Answer: They calculated g(f(2)) instead of f(g(2)), which changes the result.

Question 11: Challenge: If f(x) = x^3 and g(x) = 2x + 1, find f(g(3)) and explain each step.

Answer: g(3)=2*3+1=7; f(7)=7^3=343.