Let *f(x)* = *ax*^{7} + *bx*^{3} + *cx* – 5, where *a*, *b*, and *c* are constants.

If *f*(-7) = 7, then what is *f*(7)?

- -17
- -7
- 14
- 21
- not uniquely determined

*f(x)* = *ax*^{7} + *bx*^{3} + *cx* – 5.

*f*(-7) = *a*(-7)^{7} + *b*(-7)^{3} + *c*(-7) – 5

7 = *a*(-7)^{7} + *b*(-7)^{3} + *c*(-7) + 5 – 10

7 = –*a*(7)^{7} – *b*(7)^{3} – *c*(7) -(- 5) – 10

7 = –*f*(7) – 10

*f*(7) = -10 – 7 = -17

The answer is (a).