Let f (x)=210⋅x+1 and g(x)=310 ⋅x-1. If (fog)(x)=x, then x is equal to :

Question

Let f (x)=210⋅x+1 and g(x)=310 ⋅x-1. If (fog)(x)=x, then x is equal to : (A) (310 - 1 /310 - 2-10) (B) (210 - 1 /210 - 3-10) (C) (1 - 310 /210 - 3-10) (D) (1 - 210 /310 - 2-10)

Tardigrade Admin · Accepted Answer

f(g(x)) = x f(310x - 1) = 210(310.x - 1) = x = (1/310-2-110) 210(310x -1) + 1 = x x(610 -1) = 210 - 1 x = (210-1/610-1) =(1-2-10/310-2-10)

Q. Let $f (x) = 2^{10} \cdot x + 1$ and $g (x) = 3^{10} \cdot x - 1$ . If $(f o g) (x) = x$ , then $x$ is equal to :

$\frac{3 ^{10} - 1}{3 ^{10} - 2 ^{- 10}}$

$\frac{2 ^{10} - 1}{2 ^{10} - 3 ^{- 10}}$

$\frac{1 - 3 ^{10}}{2 ^{10} - 3 ^{- 10}}$

$\frac{1 - 2 ^{10}}{3 ^{10} - 2 ^{- 10}}$

f(g(x)) = x
$f (3^{10} x - 1) = 2^{10} (3^{10} . x - 1) = x$
$= \frac{1}{3 ^{10} - 2 ^{- 110}}$
$2^{10} (3^{10} x - 1) + 1 = x$
$x (6^{10} - 1) = 2^{10} - 1$
$x = \frac{2 ^{10} - 1}{6 ^{10} - 1} = \frac{1 - 2 ^{- 10}}{3 ^{10} - 2 ^{- 10}}$

Q. Let f(x)=210⋅x+1 and g(x)=310⋅x−1. If (fog)(x)=x, then x is equal to :

310−2−10310−1​

210−3−10210−1​

210−3−101−310​

310−2−101−210​