What is the domain and range of #f(x) =e^x#?

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Answer 1 · 2018-06-21T09:28:48

See below.

#f(x)=e^x#

This function is valid for all real #x#, so the domain is:

#color(blue)({x in RR}#

Or in interval notation:

#color(blue)((-oo,oo)#

To find the range we observe what happens as #x# approaches #+-oo#

as: #x->oo# , #color(white)(8888)e^x->oo#

as: #x->-oo# , #color(white)(8888)e^x->0#

( i.e if x is negative we have #bb(1/(e^x)#)

We also observe that #e^x# can never equal zero.

So our range is:

#color(blue)({f(x) in RR | 0 < x}#

Or

#color(blue)((0,oo)#

This is confirmed by the graph of #f(x)=e^x#

graph{y=e^x [-16.02, 16.01, -8.01, 8.01]}