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anonymous
 one year ago
Find gof if
f(x)=x+(1/x) and g(x)= (x+1)/(x+2)
anonymous
 one year ago
Find gof if f(x)=x+(1/x) and g(x)= (x+1)/(x+2)

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princeharryyy
 one year ago
Best ResponseYou've already chosen the best response.0g(f(x))= (f(x)+1)/(f(x)+2)

princeharryyy
 one year ago
Best ResponseYou've already chosen the best response.0just out the value of f(x) in place of f(x) in above equation n solve

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know that, I just am not sure how to solve it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the fraction confuses me

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4\[(g \circ f) = g\left(x+\frac{1}{x}\right) = \frac{\left(x+\dfrac{1}{x}\right)+1}{\left(x+\dfrac{1}{x}\right)+2}\]

princeharryyy
 one year ago
Best ResponseYou've already chosen the best response.0well, you got the answer now, I guess.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4That isn't the answer.

princeharryyy
 one year ago
Best ResponseYou've already chosen the best response.0that's almost the final answer @Jhannybean

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the answer would be (x^2+x+1)/(x+1)^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but i want to know how they got that answer

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4multiply both the numerator and denominator by \(x\). \[\frac{\left(x+\dfrac{1}{x}\right)+1}{\left(x+\dfrac{1}{x}\right)+2} \cdot \frac{x}{x} \]

princeharryyy
 one year ago
Best ResponseYou've already chosen the best response.0(g∘f)=g(x+1/x)=(x^2+1+x)/(x^2+2+x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is that because it is the denominator of 1/x? @Jhannybean

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so would that same thing apply to fof?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4\[(f\circ f)= f\left(x+\frac{1}{x}\right) = \left(x+\frac{1}{x}\right)+\dfrac{1}{x+\dfrac{1}{x}}\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4but when you're trying to solve this... set all that complicated junk = \(a\) or any other variable. find the common denominator, and simplify.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4\[\text{let a}=x+\frac{1}{x}\]\[(f\circ f) = a+\frac{1}{a} = \frac{a^2+1}{a} = \dfrac{\left(x+\dfrac{1}{x}\right)^2+1}{\left(x+\dfrac{1}{x}\right)} \]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4\[=\frac{x^2+\dfrac{1}{x^2}+2 +1}{\dfrac{x^2+1}{x}} =\frac{x^2+\dfrac{1}{x^2}+3}{\dfrac{x^2+1}{x}} \] So now you'd want to multiply both numerator and denominator by \(\dfrac{x}{x}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i did it a different way

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and got the answer x^4+3x^2+1/x(x^2+1)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, i understood your approach as well so thank you

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4\[\frac{x^2+\dfrac{1}{x^2}+3}{\dfrac{x^2+1}{x}} \cdot \frac{x}{x} =\frac{\dfrac{x^4+3x^2+1}{x}}{x^2+1} = \color{red}{\frac{x^4+3x^2+1}{x(x^2+1)}}\]
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