Given f(x)= 4x^2=9x+2 and g(x)=3x-2, find and simplify the following:
(f+g)(x)
(fg)(x)
(f-g)(3)
I have a few other problems i need help with too so if you want to lend me a hand let me know.
We will be happy to critique your thinking.
the standard definition of
(f+g)(x) = f(x) + g(x)
so for your functions
(f+g)(x) = (4x^2+9x+2) + (3x-2)
simplify this and then
follow the same technique for the other two questions, and let me know what you got
To find (f+g)(x), we need to add f(x) and g(x) together.
Step 1: Start by substituting f(x) and g(x) into the equation:
(f+g)(x) = f(x) + g(x)
= 4x^2 + 9x + 2 + 3x - 2
Step 2: Combine like terms:
(f+g)(x) = 4x^2 + (9x + 3x) + (2 - 2)
= 4x^2 + 12x
Therefore, (f+g)(x) = 4x^2 + 12x.
To find (fg)(x), we need to multiply f(x) and g(x) together.
Step 1: Start by substituting f(x) and g(x) into the equation:
(fg)(x) = f(x) * g(x)
= (4x^2 + 9x + 2) * (3x - 2)
Step 2: Use the distributive property to expand the expression:
(fg)(x) = 4x^2 * (3x - 2) + 9x * (3x - 2) + 2 * (3x - 2)
= 12x^3 - 8x^2 + 27x^2 - 18x + 6x - 4
Step 3: Combine like terms:
(fg)(x) = 12x^3 + (27x^2 - 8x^2) + (6x - 18x) - 4
= 12x^3 + 19x^2 - 12x - 4
Therefore, (fg)(x) = 12x^3 + 19x^2 - 12x - 4.
To find (f-g)(3), we need to subtract g(x) from f(x) using x = 3.
Step 1: Start by substituting f(x) and g(x) into the equation:
(f-g)(3) = f(3) - g(3)
= (4(3)^2 + 9(3) + 2) - (3(3) - 2)
Step 2: Solve the equations within each parenthesis:
(f-g)(3) = (4(9) + 9(3) + 2) - (9 - 2)
= (36 + 27 + 2) - (7)
= 65 - 7
Step 3: Evaluate the subtraction:
(f-g)(3) = 58
Therefore, (f-g)(3) = 58.
Please let me know if you have any further questions or if you need help with other problems! I'm here to assist you.