125k views
3 votes
Can someone tell me how to solve this? Thank you

Can someone tell me how to solve this? Thank you-example-1
User AYMADA
by
9.0k points

1 Answer

4 votes

Answer:

domain: all real numbers except x=3 and x=5.

Explanation:

You want the domain of a composition of rational functions f(x)=1/(x-2) and g(x)=4/(x-3).

Domain

The domain of a function is the set of values of the independent variable for which the function is defined.

To compute f(g(x)), you must first compute g(x). When x=3, the denominator of the function 4/(x-3) is zero, so the value is undefined. The domain must exclude x=3.

The composition is found by substituting g(x) for x in the definition of f(x).


f(g(x)) = f((4)/(x-3)) =(1)/((4)/(x-3)-2)=(x-3)/(4-2(x-3))\\\\f(g(x))=(x-3)/(4-2x+6)=(x-3)/(2(5-x))

We have written the composition in this form so you can see there is a denominator factor that will be zero when x=5. The domain of f(g(x)) must also exclude x=5.

The domain of f(g(x)) is all real numbers except x=3 and x=5.

Can someone tell me how to solve this? Thank you-example-1
User Randunel
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories