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If f(x)=x-3/x and g(x)=5x-4, what is the domain of (f•g)(x)

If f(x)=x-3/x and g(x)=5x-4, what is the domain of (f•g)(x)-example-1
User Bruce Lee
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2 Answers

3 votes

Answer:

basically C

Explanation:

User Anantha Krishnan
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5 votes

Answer:


\x\\eq (4)/(5)\

Explanation:

Given functions are,


f(x)=(x-3)/(x)-----(1)


g(x)=5x-4-----(2)

Now, by the property of composition of functions,


(fog)(x)=f(g(x))


=f(5x-4) ( From equation (2) )


=(5x-4-3)/(5x-4) ( From equation (1) )


=(5x-7)/(5x-4)

Which is a rational function,

Since, the rational function is defined for all real numbers except those real values for which denominator = 0,

If 5x - 4 = 0


\implies x = (4)/(5)

So, the function (fog) is defined for all real numbers except 4/5,

Therefore, the domain of (fog)(x) is
\x\\eq (4)/(5)\.

User Eduard
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