I wanted to double check that I am correct on the work area and answers please.
1.Given f(x)=x+2 and g(x)= 3x-4. Find (f+g).
Work: (x+2) + (3x-4)
Answer: 4x-2
2.Given f(x)=x+2 and g(x)=3x-4. Find (f*g).
Work: (x+2)(3x-4)
Answer: 3x² +2x-8
3.Given f(x)=x+2 and g(x)=3x-4. Find (f*g)(x).
Work: f(3x-4)= (3x+4)+2
Answer: 3x-2
4.Given f(x)=x+2 and g(x)= 3x-4. Find (f*g)(1).
Work: g(1)= 3(1)-4= -1
F(-1)= (-1+2)=1
Answer: 1
All answers are correct
Let's go through each question one by one to double-check the work and answers:
1. Given f(x) = x + 2 and g(x) = 3x - 4, we want to find (f + g).
The correct work is: (x + 2) + (3x - 4)
Expanding the parentheses gives: x + 2 + 3x - 4
Combining like terms, we get: 4x - 2
The answer provided, 4x - 2, is correct.
2. Given f(x) = x + 2 and g(x) = 3x - 4, we want to find (f * g).
The correct work is: (x + 2)(3x - 4)
To multiply these expressions, we need to distribute:
(x * 3x) + (x * -4) + (2 * 3x) + (2 * -4)
Simplifying, we get: 3x^2 + 2x - 8
The answer provided, 3x^2 + 2x - 8, is correct.
3. Given f(x) = x + 2 and g(x) = 3x - 4, we want to find (f * g)(x).
The correct work is: f(3x - 4) = (3x - 4) + 2
Expanding the expression inside the parentheses, we get: 3x - 4 + 2
Simplifying further gives: 3x - 2
The answer provided, 3x - 2, is correct.
4. Given f(x) = x + 2 and g(x) = 3x - 4, we want to find (f * g)(1).
The first step is to find g(1): g(1) = 3(1) - 4 = -1
Then, we can find f(-1): f(-1) = -1 + 2 = 1
The answer provided, 1, is correct.
Overall, all the answers and work shown for each question are correct. Well done!