Question

show that functions f and g defind by f(x)=2 log x and g(x)= log x^2 are not equal even through log x^2 =2 log x​

Answer 1

Answer:

for two functions to be equal, the sets of domain and ranges must be equal.

if we look at the domain of these functions

f(x) = 2logx

x can assume any positive real value because log of negative number or zero is not defined. so the domain of the function would be

{x / x€R, x>0}

now g(x) = log x^2

here, x can assume any real value except zero. because for negative real values, x^2 is positive and log function is defined. so domain of this function is

{x / x€E, x is not equal to 0}

we can see that domains of both the functions are not equal.

Hence the two functions are not equal