Home
Class 12
MATHS
Show that the exponential function f:...

Show that the exponential function `f: RvecR ,` given by `f(x)=e^x ,` is one-one but not onto. What happens if the co-domain is replaced by `R_0^+` (set of all positive real numbers).

Answer

Step by step text solution for Show that the exponential function f: RvecR , given by f(x)=e^x , is one-one but not onto. What happens if the co-domain is replaced by R_0^+ (set of all positive real numbers). by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

Show that the exponential function f:R rarr R given by f(x)=e^(x), is one-one but not onto. What happens if the co-domain is replaced by R0+( set of all positive real numbers).

Show that the function f:N rarr N, given by f(x)=2x, is one-one but not onto.

Show that the function f:N rarr N given by f(x)=3x is one one but not onto

Show that the modulus function f:R rarr R , given by f(x)=|x| is neither one-one nor onto.

Prove that the function f:RrarrR given by: f(x) = 5x is one-one and onto.

Prove that the function f:R rarr R given by f(x)=2x is one-one and onto.

Show that the Signum function f:R rarr R , given by f(x)={[1,x>00,x=0-1,x<0]) is neither one-one nor onto

Show that the function f:R rarr R given by f(x)=cos x for all x in R, is neither one- one nor onto

Show that the function f:R rarr R given by f(x)=cos x function f:R, is neither one-one nor onto.

Show that the function f:RrarrR given by : f(x)=ax+b , where a, binR, ane0 one one and onto.

Home
Profile