(f + g)(x)
(f - g)(x)
Notation
fg(x)
gf(x)
Functions and Real World Applications
(f*g)(x)
(f/g)(x)
100
f(x) = 2x g(x) = 3 (f + g)(x)=?
What is (f+g) = 2x +3.
100
f of x
What is f(x).
100

f(x) = 3x g(x) = 4 fg(x)= ?

What is fg(x) = 12.

100
You work forty hours a week at a furniture store. You receive a $220 weekly salary, plus a 3% commission on sales over $5000. Assume that you sell enough this week to get the commission. Given the function f(x) = 0.03x and g(x) = x – 5000. What is (f o g)(x) = ?
What is (f o g)(x) = 0.03x - 150.00.
100
f(x) = 4x g(x) = 2x (f * g)(x) = ?
What is (f * g)(x) = 8x²
200
f(x) = 13x g(x) = 4x (f-g) = ?
What is (f-g) = 9x.
200
g of x equals two x.
What is g(x) = 2x.
200

f(x) = -2 g(x) = 5x gf(x)= ?

What is gf(x) = -10.

200
You work forty hours a week at a furniture store. You receive a $220 weekly salary, plus a 3% commission on sales over $5000. Assume that you sell enough this week to get the commission. Given the function f(x) = 0.03x and g(x) = x – 5000. What is (g o f)(x) = ?
What is (g o f)(x) = 0.03x - 5000.
200
f(x) = 4x g(x) = 2x (f/g)(x) = ?
What is (f/g)(x) = 2.
300
f(x) = 8x + 2 g(x) = 2x (f-g)(x) = ?
What is (f-g)(x)=6x+2.
300
"f composed with g of x"
What is (f o g)(x)
300

f(x) = 3x g(x) = 2x + 5 fg(x)= ?

What is fg(x) = 6x + 15.

300
The number N of bacteria in a refrigerated food is given by N(T) = 20T² – 80T + 500, 2 ≤ T ≤14 where T is the temperature of the food in degrees Celsius. When the food is removed from refrigeration, the temperature of the food is given by T(t) = 4t + 2, 0 ≤ t ≤3 where t is the time in hours. Find the composition N(T(t)) and interpret its meaning in context.
What is N(T(t)) = 20(4t + 2)² – 80(4t + 2) + 500 = 20(16t² + 16t + 4) – 320t – 160 + 500 = 320t² + 320t + 80 – 320t – 160 + 500 = 320t² + 420 The composite function N(T(t)) represents the number of bacteria in the food as a function of the amount of time the food has been out of refrigeration.
300
f(x) = 3x + 5 g(x) = 2x + 6 (f*g) = ?
What is (f*g)(x) = 6x² +25x + 25.
400
f(x) = 4x + 5 g(x) = 2x + 8 (f+g)(x)=?
What is (f+g) = 6x + 13.
400
Explain the difference between f(g(x)) and g(f(x)).
What is f(g(x)) means you put g into f everywhere there is an x and g(f(x)) means you put f into g everywhere there is an x.
400

f(x) = 9x g(x) = 5x + 2 fg(x)= ?

What is fg(x) = 45x +18.

400
You make a purchase at a local hardware store, but what you’ve bought is too big to take home in your car. For a small fee, you arrange to have the hardware store deliver your purchase for you. You pay for your purchase, plus the sales taxes, plus the fee. The taxes are 7.5% and the fee is $20. f(x) = 1.075x is function for the total, after taxes, on purchase amount x. g(x) = x + 20 is a function for the total, including the delivery fee, on purchase amount x. Find f(g(x)) and g(f(x)). Which results in a lower cost to you?
What is f(g(x)) = (f o g)(x) = 1.075 (x +20) = 1.075x + 21.50 g(f(x)) = (g o f)(x) = (1.075x) + 20 which costs less.
400
f(x) = 25x² + 5 g(x) = 5x (f/g)(x) = ?
What is (f/g)(x) = 5x + 1.
500
f(x) = x² + 5x +3 g(x) = 3x² + 10x - 10 (f+g)(x) = ?
What is (f+g)(x)=4x² + 15x - 7.
500
Explain the notation (f+g)(x), (f-g)(x), (f*g)(x), and (f/g)(x).
What is... you take the two functions f(x) and g(x) and perform the indicated operations such as addition, subtraction, multiplication, or division.
500

f(x) = 4x + 3 g(x) = 2x^2 + 1 gf(x)= ?

What is gf(x) = 32x^2 + 48x + 19.

500
You work forty hours a week at a furniture store. You receive a $220 weekly salary, plus a 3% commission on sales over $5000. Assume that you sell enough this week to get the commission. Given the function f(x) = 0.03x and g(x) = x – 5000, which of (f o g)(x) and (g o f)(x) represents your commission?
Using (f o g)(x) = f(g(x)) means subtract the sales x from $5000 that didn't earn commission, and then multiplying by 3%. On the other hand, (g o f)(x) = g(f(x)) means multiply the sales x by 3%, and then subtract $5000 from the result. This could result in a negative number Therefore, (f o g)(x) represents the commission.
500
f(x) = x² + 5x +2 g(x) = 3x +2 (f*g)(x)=?
What is (f*g)(x) = 3x^3 + 17x² + 16x + 6.
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