if f(x) = 7/x+5 and g(x) = 1/x what is (fog)(x)

This question is what we called composite functions in Mathematics. A composite function is defined as applying one function to the results of another. If we say the result of f() is sent through g(), we can express mathematically as follows: 

Which translates as the following: 

And vice versa, like in our example, we say the result of g() is send through f():

which translates as: 

PLEASE...

This question is what we called composite functions in Mathematics. A composite function is defined as applying one function to the results of another. If we say the result of f() is sent through g(), we can express mathematically as follows: 

Which translates as the following: 

And vice versa, like in our example, we say the result of g() is send through f():

which translates as: 

PLEASE NOTE:    is NOT equal to  

Now let's answer our question:

Now write what we solving for as shown above: 

Now where ever you see x substitute g(x):

We know the value of g(x), now we substitute it 

 

We can simplify this to get rid of the fraction in the denominator.  Multiply 5 by x/x to get a common denominator and then add them together.

We can simplify this more by multiplying the numerator and the denominator by x.  This will get rid of the fraction in the denominator.

SUMMARY: 

• Convert  into 

 

• ANSWER: 


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