Question

let f:R^+ -> R^+ is a maping defined by f(x)=e^x. Show that f is bijective mapping​

Answer 1

Answer:

here is ur answer

Step-by-step explanation:

f : R^+ --> R^+

f(x)= e^x

proving it is one-one:

by derivative method we have d(e^x)/dx = e^x which is always positive since it is exponential function.

hence it is one one as derivative is always >=0

proving it is onto:

as e^x is exponential function, its value cant be less than zero.

hence range lies between 0 to  +infinity

hence range = co-domain of the function = R^+

hence it is onto

so, it is bijective as it is both one-one and onto