Question

Solve the domain of this function f(x) =log100x [{2log10(x) +1}] /-x]?

Answer 1

Answer:

0 < x  <  1/√10

Step-by-step explanation:

f(x) =log100x [{2log10(x) +1}] /-x]?

log10(x) is defined if x is +ve  =>  x> 0

{2log10(x) +1}] /-x  > 0

=> 2log10(x) +1  < 0   as x > 0

=> 2log10(x)  <  - 1

=> log10(x) < - 1/2

=>  x < 10^(-1/2)

=> x  <  1/10^(1/2)

=> x  <  1/√10

0 < x  <  1/√10

Domain of function f(x) =log100x [{2log10(x) +1}] /-x]  is 0 < x  <  1/√10