(a)

Yes, the function g is one - to - one.

Because each European shoe size corresponds to exactly one U.S. shoe size.

(b)

Each U.S. shoe size 6 corresponds to exactly European shoe size 38.

So, .

The value of .

(c)

Each European shoe size 42 corresponds to exactly U.S. shoe size 9.

So, .

The value of .

(d)

Find .

Each European shoe size 39 corresponds to exactly U.S. shoe size 7.

Since , .

Each U.S. shoe size 7 corresponds to exactly European shoe size 39.

Since , .

The value of .

(e)

Find .

Each U.S. shoe size 5 corresponds to exactly European shoe size 37.

Since , .

Each European shoe size 37 corresponds to exactly U.S. shoe size 5.

Since ,  .

The value of .

(a)

Yes, the function g is one - to - one.

(b)

The value of .

(c)

The value of .

(d)

The value of .

(e)

The value of .