for the given functions f and g, find the specified value of the following functions and state the domain of each one. f(x)=2+3/x; g(x)=3/x
a.(f-g)(2)=
b.(f/g)(3)=
how do I do this? I need help! it throws me off because of it being in fraction form.
(f - g)(2)
= f(2) - f(2)
= 2 + 3/2 - 3/2 = 2
(f/g)(2)
= (2+3/2) / (3/2)
= (7/2) / (3/2)
= (7/2)(2/3) = 7/3
thank you so much....what would be the domains of these though?
To find the value of the functions and their domains, you can follow these steps:
Step 1: Evaluate f(x) and g(x)
For f(x)=2+3/x, plug in x=2 to find f(2).
f(2) = 2+3/2 = 2 + 1.5 = 3.5
For g(x)=3/x, plug in x=2 to find g(2).
g(2) = 3/2 = 1.5
Step 2: Calculate (f-g)(2)
To find (f-g)(2), subtract the values of f(2) and g(2).
(f-g)(2) = f(2) - g(2) = 3.5 - 1.5 = 2
Step 3: Simplify (f/g)(3)
To find (f/g)(3), divide the values of f(3) by g(3).
(f/g)(3) = f(3) / g(3)
Now, substitute f(x) and g(x) into the equation:
(f/g)(3) = (2 + 3/3) / (3/3)
= (2 + 1) / 1
= 3
Step 4: Determine the domains
The domain of a function is the set of all numbers for which the function is defined.
For f(x) = 2 + 3/x, the function is defined for all x ≠ 0. Therefore, the domain is (-∞, 0) U (0, ∞).
For g(x) = 3/x, the function is defined for all x ≠ 0. Hence, the domain is (-∞, 0) U (0, ∞).
For both (f-g)(2) and (f/g)(3), since they are obtained by evaluating f(x) and g(x) at specific values, the domain is the same as for f(x) and g(x), which is (-∞, 0) U (0, ∞).