for the given functions f and g, find the specified value of the following functions and state their domains:
f(x)=x-5; g(x)=2x^2
a.(f+g)(3)=
b.(f/g)(3)=
Can someone help me figure this out? pleeeease????
form your functions,
(f+g)(x) = x-5 + 2x^2
so (f+g)(3) = 3-5+50 = 48
do the same thing for your second question
Sure! I'd be happy to help you figure this out step-by-step.
a. To find (f+g)(3), we need to first evaluate f(3) and g(3) individually, and then add them together.
First, let's find f(3):
f(x) = x - 5
f(3) = 3 - 5
f(3) = -2
Next, let's find g(3):
g(x) = 2x^2
g(3) = 2(3)^2
g(3) = 2(9)
g(3) = 18
Now, let's add the values we found together:
(f+g)(3) = f(3) + g(3)
(f+g)(3) = (-2) + (18)
(f+g)(3) = 16
So, (f+g)(3) = 16.
The domain of (f+g)(x) would be the intersection of the domains of f(x) and g(x), which is all real numbers since both f(x) and g(x) are defined for all real numbers.
b. To find (f/g)(3), we need to first evaluate f(3) and g(3) individually, and then divide them.
First, let's find f(3) once again:
f(x) = x - 5
f(3) = 3 - 5
f(3) = -2
Next, let's find g(3) once again:
g(x) = 2x^2
g(3) = 2(3)^2
g(3) = 2(9)
g(3) = 18
Now, let's divide the values we found:
(f/g)(3) = f(3) / g(3)
(f/g)(3) = (-2) / 18
(f/g)(3) = -1/9
So, (f/g)(3) = -1/9.
The domain of (f/g)(x) would be the set of all real numbers except for any value of x that makes the denominator equal to zero. Since g(x) = 2x^2, the domain would be all real numbers except x = 0.
Of course, I'll be happy to help you out!
To find the specified value of a function, we need to substitute the given value into the function. Let's start by solving part (a).
a. To find (f+g)(3), we need to find the sum of f(x) and g(x) when x = 3. Let's substitute x = 3 into the functions f(x) and g(x) first:
f(3) = 3 - 5 = -2
g(3) = 2(3)^2 = 2(9) = 18
Now, let's find (f+g)(3) by adding these two values:
(f+g)(3) = f(3) + g(3) = -2 + 18 = 16
So, (f+g)(3) = 16.
Now, let's move on to part (b).
b. To find (f/g)(3), we need to find the quotient of f(x) and g(x) when x = 3. Let's substitute x = 3 into the functions f(x) and g(x):
f(3) = 3 - 5 = -2
g(3) = 2(3)^2 = 2(9) = 18
Now, let's find (f/g)(3) by dividing these two values:
(f/g)(3) = f(3) / g(3) = -2 / 18
To simplify this fraction, we can divide the numerator and denominator by their greatest common divisor, which is 2:
(f/g)(3) = (-2/2) / (18/2) = -1 / 9
So, (f/g)(3) = -1/9.
Now, let's state the domains of these functions.
The domain of a function describes all the possible input values that the function can take. In the case of both f(x) = x - 5 and g(x) = 2x^2, the domain is all real numbers because there are no restrictions on the values of x that we can plug into these functions.
Therefore, for both functions f(x) and g(x), the domain is (-∞, +∞).
I hope this helps you understand how to find the specified values of functions and determine their domains! Let me know if there's anything else I can assist you with.