Question

若y=f（x）是冪函數，且滿足

f(4)

f(2)

=

2

2

，則f（3）=______．

Answer 1

設冪函數f（x）=x^α，則

f(4)

f(2)

=

2

2

=

4α

2α

=2^α，∴α=-

1

2

，
∴f（3）=3-

1

2

=

1

3

=

3

3

，
故答案為

3

3

．