Question

Find the domain of f(g(x)). f(x)= 5/x-1 g(x)=4/3x-2 If anyone can solve this and explain the...

Find the domain of f(g(x)). f(x)= 5/x-1 g(x)=4/3x-2

If anyone can solve this and explain the steps I would greatly appreciate it. I found an answer but I want to check if I did it correctly.

Math   Precalculus   
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Homework Answers

Answer #1

f(x) = 5 / (x - 1)

g(x) = 4 / (3x - 2)

Therefore,

f(g(x))

= f(4 / (3x - 2))

= 5 / ((4 / (3x - 2)) - 1)

= 5 (3x - 2) / (4 - 3x + 2)

= 5 (3x - 2) / (6 - 3x)

Domain is the set of real values of x for which the function is real and defined.

In this case, for f(g(x)) to be real and defined, the denominator must not be equal to 0

Therefore,

6 - 3x 0

=> 3x 6

=> x 2

Therefore,

Domain is (- , 2) U (2, )

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