What is the domain and range of $f (x) = e^{x}$ $f(x) =e^x$ ?

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Answer 1 · 2018-06-21T09:28:48

See below.

$f (x) = e^{x}$ $f(x)=e^x$

This function is valid for all real $x$ $x$ , 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]}

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