Answer:
The domain is {x I x ≠ 13} ⇒ the last answer
Step-by-step explanation:
* Lets talk about the composite function
- It is a function is found from two given functions by applying one
function into the second function.
- The applying function is the domain of the second function
- (f °g)(x) means g(x) is applying into f(x)
* Lets solve the problem
∵ f(x) = x + 7
∵ g(x) = 1/(x -13)
- To apply g(x) into f(x) replace x in f(x) by g(x)
∴ f(g(x)) = f(1/(x - 13)) = 1/(x - 13) + 7
- The domain of the function is all values of x which make the function
defined
- The domain is all real numbers except the value which makes
the denominator = 0
- To find this value put the denominator = 0
∵ The nominator of (f ° g)(x) is x - 13
∴ Put x - 13 = 0
∴ x - 13 = 0 ⇒ add 13 to both sides
∴ x = 13
∴ The domain of (f ° g)(x) is all real numbers except x = 13
* The domain is {x I x ≠ 13}
