Find the specified value of the following functions and state the domain of each one.
f(x)=x-11;g(x)=7x^2
(a) (f+g)(5)=
(f+g)(x) = 7 x^2 + x - 11
if x = 5
7(25) + 5 - 11
= 169
To find the value of (f + g)(5), we need to first find the individual values of f(5) and g(5), and then add them together.
For f(x) = x - 11:
Substitute x = 5 into the function:
f(5) = 5 - 11 = -6
For g(x) = 7x^2:
Substitute x = 5 into the function:
g(5) = 7(5)^2 = 7(25) = 175
Next, we add the values together to find (f + g)(5):
(f + g)(5) = f(5) + g(5) = -6 + 175 = 169
Therefore, (f + g)(5) = 169.
Now let's determine the domain of each function:
For f(x) = x - 11:
Since this is a polynomial function, the domain is all real numbers. Therefore, the domain of f(x) is (-∞, ∞).
For g(x) = 7x^2:
Again, since this is a polynomial function, the domain is all real numbers. So, the domain of g(x) is also (-∞, ∞).