“set -e” in a function

Question

How can I use set -e semantics in a function?

This is reopen to "set -e" in a function question since it has not been answered correctly and has already been accepted.

Here is example:

#!/bin/bash
set -exo pipefail
f() {
    echo a
    false
    echo Should NOT get HERE
}
if f ; then
    true
fi

I would like f to exit at false.

My experiments show that using subshell (f) call doesn't help here:

#!/bin/bash
set -exo pipefail
f() {
    echo a
    false
    echo Should NOT get HERE
}
g() {   
    ( f )
}
if g ; then
    true
fi

Moving f out of the if statement does the job of course in this particular case:

#!/bin/bash
set -exo pipefail
f() {
    echo a
    false
    echo Should NOT get HERE
}
f
if [ "$?" != "0" ] ; then
    true
fi

This doesn't help me that much tough.

Is it possible to turn on set -e semantics when the function is executed from within the if predicate?