if f(x)=2x and g(x)= x+1 , what do you think someone means by (f+g)(x)? what about (f/g)(x)?
When someone writes (f+g)(x), they are usually referring to the sum of the functions f(x) and g(x) evaluated at a specific value of x. To find (f+g)(x), you simply add the values of f(x) and g(x) at that particular x.
In this case, f(x) = 2x and g(x) = x + 1. Therefore, (f+g)(x) would be the sum of these two functions. Mathematically, we can express it as:
(f+g)(x) = f(x) + g(x)
= 2x + (x + 1)
To simplify further, combine like terms:
(f+g)(x) = 2x + x + 1
= 3x + 1
So, (f+g)(x) is equal to 3x + 1.
Similarly, when someone writes (f/g)(x), they are referring to the quotient of the functions f(x) and g(x) evaluated at a specific value of x. To find (f/g)(x), you divide the value of f(x) by the value of g(x) at that particular x.
Using the same functions f(x) = 2x and g(x) = x + 1, we can express (f/g)(x) as:
(f/g)(x) = f(x) / g(x)
= (2x) / (x + 1)
To simplify further, we use the concept of division by a fraction, where we multiply the numerator by the reciprocal of the denominator:
(f/g)(x) = (2x) * (1 / (x + 1))
Combining terms, we have:
(f/g)(x) = 2x / (x + 1)
So, (f/g)(x) is equal to 2x / (x + 1).