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

Answer: 11

Question 2: Given f(x) = 3x and g(x) = x + 5, find the value of f(g(2)).

Answer: 21

Question 3: Construct the composite function f(g(x)) where f(x) = x^2 and g(x) = 2x + 1. Write a simplified expression for f(g(x)).

Answer: (2x + 1)^2

Question 4: Plot the graph of y=2x on the grid. Then, calculate f(g(3)) if f(x) = 4x and g(x) = 2x.

Answer: f(g(3))=24

Question 5: A toy car moves according to the function d(t) = 5t, where t is time in seconds. The speed function is s(t) = 2t + 1. Find the position of the car after 4 seconds using the composite function d(s(t)).

Answer: d(s(4))= d(2*4+1)= d(9)=45

Question 6: If f(x) = x/2 and g(x) = 4x + 2, evaluate f(g(5)).

Answer: 11

Question 7: Identify the mistake in the following calculation: Given f(x)=x+3 and g(x)=x^2, the student calculates f(g(2)) as 2^2 + 3=7. Explain the error and correct it.

Answer: Incorrect; f(g(2))= (2)^2 + 3=4+3=7 (correct). Mistake in reasoning if the student thought f(g(x))=g(x)+3.

Question 8: Given functions f(x)=x+2 and g(x)=3x, find f(g(x)) and simplify.

Answer: f(g(x))=3x+2

Question 9: A roller coaster's height function is h(t) = 4t^2 + t, and its velocity function is v(t) = 8t + 1. Find the height after 3 seconds using the composite h(v(t)).

Answer: h(v(3))= h(8*3+1)= h(25)=4*(25)^2 +25=4*625+25=2500+25=2525

Question 10: Evaluate the composite function where f(x)=x^3 and g(x)=x-2 at x=5.

Answer: f(g(5))= (5-2)^3=3^3=27

Question 11: Challenge: If f(x) = x^2 - 1 and g(x) = 3x + 4, find the value of x such that f(g(x)) = 8.

Answer: g(x)= ±√(8+1)= ±3; g(x)=3x+4=±3; x=(±3-4)/3= (-1/3) or (-7/3)