Question

If f(x)=x/[sqrt(1-x^2)],
then (fofof)(x)=

Answer 1

hi friend,

f(x)=x/√(1-x²)

→f(f(x))=[ x/√(1-x²)]/√(1-(x/√(1-x²))²)

→[x/√(1-x²)]/√(1-(x²/1-x²))

→[x/√(1-x²)]/√(1-2x²/1-x²)

→x/√(1-2x²)

now ,f(f(f(x)))=[x/√(1-x²)]/√(1-2(x/√(1-x²)²)

→[x/√(1-x²)]/√(1-(2x²/1-x²))

→[x/√(1-x²)]/√(1-3x²/1-x²)

→x/√(1-3x²)


I hope this will help u :)

Answer 2

f(x) = x/√ ( 1 -x²)

f( f( x)) = f(x)/√{ 1 - f(x)² }

= x/√(1 - x²)/√{ 1 -x²/( 1 -x²) }

= x/√(1 -x²)/√( 1 - x² - x²)/√(1 -x²)

= x/√( 1 -2x²)

f( f( f(x)) = f(f(x))/√( 1 - f(f(x)²)

= x/√( 1 - 2x²)/√{ 1 - x²/( 1- 2x²)}

= x/√(1 - 3x²)

so, ( fofofo)x = f(f(f(x)) = x/√(1 -3x²)