Let f(x) = 210.x + 1 and g(x)=310.x - 1.

Question

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

Accepted Answer

(fog) (x)   =   x

$$ \Rightarrow $$ $\,\,\,$f (g(x))   =   x$ \Rightarrow $$ $\,\,\,$$ f (310. x - 1)   =   x    [ as    g(x) = 310. x - 1]

$$ \Rightarrow $$ $\,\,\,$210 . (310 . x$-$1) + 1   =   x$ \Rightarrow $$ $\,\,\,$$ 310 . x - 1 + 2-10   =   x . 2-10   [dividing by 210]

$$ \Rightarrow $$ $\,\,\,$310 . x$-$2$-$10 . x   =   1$-$2$-$10$ \Rightarrow $$ $\,\,\,$$ x (310 - 2- 10)   =   1- 2-10

$$ \Rightarrow $$ $$\,\,\,$$ x = $${{1 - {2^{ - 10}}} \over {{3^{10}} - {2^{ - 10}}}}$$

Solutions · 1