How would you solve this?
1.(f+g)(3)
depends on f and g, but it means f(3) + g(3)
f(x)=x^2+3 and g(x)=3x-1
So would i multiply everything by 3 First?
I multiplied everything by 3.
Is the answer 3x^2+6x-3
f(3) is the value when 3 is substituted for x. It is not a multiplication.
f(x) = x^2+3
f(3) = 3^2 + 3 = 9+3 = 12
g(x) = 3x-1
g(3) = 3*3-1 = 9-1 = 8
(f+g)(x) = f(3)+g(3) = 12+8 = 20
or, you can do the addition first
(f+g)(x) = f(x)+g(x) = x^2+3 + 3x-1 = x^2 + 3x + 2
(f+g)(3) = 3^2 + 3*3 + 2 = 9 + 9 + 2 = 20
To solve this expression, (f+g)(3), you need to substitute the value of 3 into the function (f+g). Let's go through the steps:
1. Start by replacing the variable 'f' and 'g' with their given functions. For example, let's say f(x) = 2x and g(x) = x^2.
2. Now, substitute the value of 3 into both functions.
- Substitute 3 into f(x): f(3) = 2(3) = 6.
- Substitute 3 into g(x): g(3) = (3)^2 = 9.
3. Next, substitute these values back into the expression (f+g)(3):
- (f+g)(3) = 6 + 9 = 15.
Therefore, the solution to (f+g)(3) is 15, given the specific functions for f and g.