Question

Following for the given functions. f(x)=(2)/(x),g(x)=(4)/(x^(2)-1) (a) (f+g)(x)

Answer 1

To find the sum of the functions f(x) and g(x), you simply add them together:

(f + g)(x) = f(x) + g(x)

f(x) = 2/x

g(x) = 4/(x^2 - 1)

Now, add these two functions together:

(f + g)(x) = (2/x) + (4/(x^2 - 1))

However, we should note that x^2 - 1 can be factored as (x + 1)(x - 1), so we can rewrite g(x) as follows:

g(x) = 4/[(x + 1)(x - 1)]

Now, we can combine the fractions with a common denominator:

(f + g)(x) = [2(x - 1) + 4]/[x(x + 1)(x - 1)]

Simplify the numerator:

(f + g)(x) = [2x - 2 + 4]/[x(x + 1)(x - 1)]

Combine like terms in the numerator:

(f + g)(x) = (2x + 2)/[x(x + 1)(x - 1)]

So, the sum of the functions f(x) and g(x) is:

(f + g)(x) = (2x + 2)/[x(x + 1)(x - 1)]

Explanation: