How to determine that function is one one or many one

Let g:[1,3]rarrY bae a function defined as g(x)=In(x^2+3x+1) .Then Determine whether g(x) is one -one or many one.

Determine if each function is one-one. To each person on the earth assign the number which corresponds to his age.

Determine if each function is one-one. To each country in the world which has a prime minister assign its prime minister.

Determine if each function is one-one. To each country in the world assign the latitude and longitude of its capital.

Find whether the following functions are one-one or many-one f(x)=sqrt(1-e^(1/x-1))

Find whether the following functions are one- one or many-one f(x)=sqrt(1-e^((1)/(x)-1))

Examine whether the following functions are one-one, many-one or into, onto f(x)=x^(2)+lnx

Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) such that m!=n 1) f is one one into function2) f is one one onto function3) f is many one into funciton4) f is many one onto function then

Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) such that m!=n 1) f is one one into function2) f is one one onto function3) f is many one into funciton4) f is many one onto funcionn then