Can you check my work and tell me if I did anything wrong?
1. With the functions: f(x) = x^2 + 3x and g(x) = -3 + x what is f(x) + g(x)?
Answer: x^2 + 4x - 3
2. With the functions: f(x) = x + 4 and g(x) = x -3 what is (f*g)(x)?
Answer: x^2 + x - 12
3. With the functions: f(x) = x^2 - 9 and g(x) = x - 3 what is (f/g)(x)?
Answer:x - 3
4. With the functions: f(x) = a^2 - 2ab + b^2c and g(x) = -3b^2c + 6ab what is (f-g)(x)?
Answer: a^2 - 8ab + 4b^2c
#1 ok
#2 ok
#3 Almost
x^2-9 = (x+3)(x-3)
divide by (x-3) and you are left with (x+3)
#4 ok
Thank you! (:
To check your work, we'll go through each question and compare your answers with the correct answers.
1. With the functions: f(x) = x^2 + 3x and g(x) = -3 + x, you want to find f(x) + g(x).
To get the sum of two functions, you simply add their corresponding terms. So, f(x) + g(x) would be (x^2 + 3x) + (-3 + x).
Simplifying this expression, we get: x^2 + 3x - 3 + x.
Your answer, x^2 + 4x - 3, is correct.
2. With the functions: f(x) = x + 4 and g(x) = x - 3, you want to find (f * g)(x).
To find the product of two functions, you multiply their expressions. So, (f * g)(x) would be (x + 4)(x - 3).
Expanding this expression using the distributive property, we get: x^2 - 3x + 4x - 12.
Simplifying further, we have: x^2 + x - 12.
Your answer, x^2 + x - 12, is correct.
3. With the functions: f(x) = x^2 - 9 and g(x) = x - 3, you want to find (f/g)(x).
To find the quotient of two functions, you divide their expressions. So, (f/g)(x) would be (x^2 - 9) / (x - 3).
Simplifying this expression, we have: (x - 3)(x + 3) / (x - 3).
Notice that (x - 3) cancels out in the numerator and denominator, leaving us with: x + 3.
Your answer, x - 3, is incorrect. The correct answer is x + 3.
4. With the functions: f(x) = a^2 - 2ab + b^2c and g(x) = -3b^2c + 6ab, you want to find (f - g)(x).
To find the difference of two functions, you subtract their expressions. So, (f - g)(x) would be (a^2 - 2ab + b^2c) - (-3b^2c + 6ab).
Expanding this expression by distributing the negative sign, we get: a^2 - 2ab + b^2c + 3b^2c - 6ab.
Combining the like terms, we have: a^2 - 8ab + 4b^2c.
Your answer, a^2 - 8ab + 4b^2c, is correct.
Overall, you got 3 out of 4 questions correct, and only question 3 needs correction. Keep up the good work!