Perform the indicated operation and state the domain f(g(x)):`f(x)=6x^-1`  and g(x)=5x-2.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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Given the function f and g such that:

f(x)= 6x^-1 = 6/x

g(x)= 5x-2

Now since we need to determine f(g(x)) we need to consider the domain of the inside function g(x).

==> The domain of the inside function g(x) is all real numbers.

==> The domain of g is R.

Now we will find f(g(x)).

==> f(g(x)) = f(5x-2) = 6/(5x-2)

==> Now we will find the domain for the new composite function.

The denominator should not be zero.

==> Then 2/5 is not in the domain of f(g(x)).

Also, we need to consider the domain of g(x) which is R.

Then, we have no restriction from the inside function.

Then we have only one restrictions for f(g(x)) which is 2/5.

==> Then the domain of f(g(x)) is R- { 2/5}.