Let f ( x )= ln ( e x +1) and g 1( x )= f ( x ) and g n +1( x )= f ( g n ( x )) ∀ n ≥ 1. Then the number of real roots of the equation g 10( x )= x is

Question

Let f ( x )= ln ( e x +1) and g 1( x )= f ( x ) and g n +1( x )= f ( g n ( x )) ∀ n ≥ 1. Then the number of real roots of the equation g 10( x )= x is (A) 8 (B) 4 (C) 2 (D) 0

Tardigrade Admin · Accepted Answer

g 1( x )= ln ( e x +1) g 2( x )= f ( ln ( e x +1))= ln ( e x +2) text so g 3( x )= ln ( e x +3) ldots . ., g 10( x )= ln ( e x +10)

Q. Let $f (x) = ln (e^{x} + 1)$ and $g_{1} (x) = f (x)$ and $g_{n + 1} (x) = f (g_{n} (x)) \forall n \geq 1$ . Then the number of real roots of the equation $g_{10} (x) = x$ is

8

4

2

0

$g_{1} (x) = ln (e^{x} + 1)$
$g_{2} (x) = f (ln (e^{x} + 1)) = ln (e^{x} + 2)$
$so g_{3} (x) = ln (e^{x} + 3) \dots .., g_{10} (x) = ln (e^{x} + 10)$

Q. Let f(x)=ln(ex+1) and g1​(x)=f(x) and gn+1​(x)=f(gn​(x))∀n≥1. Then the number of real roots of the equation g10​(x)=x is

8

4

2

0

g1​(x)=ln(ex+1) g2​(x)=f(ln(ex+1))=ln(ex+2) so g3​(x)=ln(ex+3)…..,g10​(x)=ln(ex+10)

Q. Let $f (x) = ln (e^{x} + 1)$ and $g_{1} (x) = f (x)$ and $g_{n + 1} (x) = f (g_{n} (x)) \forall n \geq 1$ . Then the number of real roots of the equation $g_{10} (x) = x$ is

$g_{1} (x) = ln (e^{x} + 1)$
$g_{2} (x) = f (ln (e^{x} + 1)) = ln (e^{x} + 2)$
$so g_{3} (x) = ln (e^{x} + 3) \dots .., g_{10} (x) = ln (e^{x} + 10)$