It Isn't A g f ( x ) gf(x)

Algebra Level pending

{ f ( x ) = 1 − 1 x g ( x ) = a x 2 − a 2 h ( x ) = ( f ∘ g ) ( x ) \large \begin{cases} f(x) =\displaystyle{1-\frac{ 1 }{ x }} \\\\ g(x) ={\displaystyle \frac{a}{ { x }^2 -a ^{ 2 } } } \\\\ h(x) =(f\circ g)(x) \end{cases} Given the system of functions above, find the value of a a such that h ( x ) = x 2 h(x)=x^2 .


The answer is -1.

Ervin Tronati by Ervin Tronati , 22, Italy

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Rushikesh Jogdand
Jun 25, 2016

h ( x ) = f ( g ( x ) ) = f ( a x 2 − a 2 ) = 1 − x 2 − a 2 a = 1 + a − x 2 a h(x)=f(g(x))=f\left(\frac{a}{{x}^2-a^{2}}\right)=1-\frac{x^2-a^2}{a}=1+a-\frac{x^2}{a} ∴ 1 + a − x 2 a = x 2 ⇒ 1 + a = x 2 ( 1 + 1 a ) \therefore 1+a-\frac{x^2}{a}=x^2 \Rightarrow 1+a=x^2\left(1+\frac{1}{a}\right) Since we can take any arbitrary value for x x , its coefficient must be 0 0 . ∴ a = − 1 \therefore\boxed{a=-1}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

@Kartik Malik Can u send me ur paper of technothlon ?

Kaustubh Miglani - 3 years, 11 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...