Question

Let $f\left(x\right)=2^{100}x+1$
$g\left(x\right)=3^{100}x+1$
Then the set of real numbers x such that $f\left(g\right(x\left)\right)=x$ is

• A. Empty
• B. A singleton
• C. A finite se with more than one element
• D. Infinite

Answer 1

The correct option is B A singleton

$f\left(g\right(x\left)\right)=2^{100}(3^{100}x+1)+1=x$

$\Rightarrow x(6^{100}-1)=-(1+2^{100})$

Clearly there is just one of value of x satisfying this equation. Option B is correct.