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Which of the two functions are equal?

  • Option 1)

    f(x)=\log x\: ;\: g(x)=\log x

     

     

     

  • Option 2)

    f(x)=e^{x};g(x)=2.7^{x}

  • Option 3)

    f(x)=\frac{x^{2}-y}{x-2};g(x)=x+2,x\pm 2

  • Option 4)

    f(x)=\ln x^{2}\: ;\: g(x)2\ln x

 

Answers (1)

best_answer

As we learned 

 

Equality of function -

The two function f and g are said to be equal

iff :     dom (f) = dom (g)

and     Co-dom (f) =Co - dom (g)      

and    f(x) = g (x)         x \in Domain

-

 

 f(x)=\frac{x^{2}-4}{x-2} is defined \forall x\neq 2

lly g(x) is also defined \forall x\neq 2

Thus f(x) and g(x) are equal. 

 


Option 1)

f(x)=\log x\: ;\: g(x)=\log x

 

 

 

Option 2)

f(x)=e^{x};g(x)=2.7^{x}

Option 3)

f(x)=\frac{x^{2}-y}{x-2};g(x)=x+2,x\pm 2

Option 4)

f(x)=\ln x^{2}\: ;\: g(x)2\ln x

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Himanshu

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