solve for the domain, interval notation
f(x)=(x+8)/(x^2 -49)
domain: all real numbers, except +-7
range: net inf to pos infinity. see graph https://www.wolframalpha.com/input/?i=plot+(x%2B8)%2F(x%5E2-49)
To find the domain of a function, we need to identify all the values of x for which the function is defined. In this case, we have the function f(x) = (x+8)/(x^2 - 49).
To determine the domain, we need to consider any values of x that could result in an undefined expression or division by zero. In this case, the function will be undefined if the denominator, x^2 - 49, equals zero.
To find when x^2 - 49 = 0, we can solve the equation:
x^2 - 49 = 0
Using the difference of squares factorization, we can rewrite the equation as:
(x + 7)(x - 7) = 0
Now, we set each factor to zero and solve for x:
x + 7 = 0 or x - 7 = 0
Simplifying each equation:
x = -7 or x = 7
Now, we have two values that make the denominator zero, x = -7 and x = 7. These are the values that we need to exclude from the domain.
Therefore, the domain of the function f(x) = (x+8)/(x^2 - 49) is all real numbers except x = -7 and x = 7.
In interval notation, we can express the domain as:
(-∞, -7) ∪ (-7, 7) ∪ (7, ∞)