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Let R be the set of all real numbers . If f:R-R is giev by f(x)=3x + 2, for all x belongs to R and g:R-R is given by g(x)= x/x^2 + 1 , for all x belongs to R find the following f°g, g°f, f°f and g°g .

Posted by Arnab H. 3 years, 6 months ago

CBSE > Class 12 > Mathematics

2 answers

Arnab H. 3 years, 6 months ago

Thank you so much . ??

1Thank You

Arpit Airen 3 years, 6 months ago

Here I will tell you how to find F0g & hope you will find the remaining.

f0g is pronounced as f of g(x)

f0g = f{g(x)} = f {{tex}x \over x^2 +1{/tex}}

We have put the value of g(x) given in question.

Now let us assume that {tex}{x \over x^2 +1} = y{/tex}

Therefore, f {{tex}x \over x^2 +1{/tex}} = f{y}

as f{x} = 3x+2

f{y} = 3y +2

Therefore

f{{tex}{x \over x^2 +1}{/tex}} = 3 * {tex}{x \over x^2 +1}{/tex} + 2

=> f0g = {tex}{3x \over x^2 +1} +2 {/tex}

On Solving

f0g = {tex}{3x + 2x^2 +2\over x^2 +1}{/tex}

Answer.

1Thank You

ANSWER

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