Calculate f(-7) if f(7)=7 f(x)= ax^7 + bx^3 + cx - 7

If f(x)=a*x^7 + b*x^3 + c*x – 7,
then

f(-x)= a*(-x)^7 + b*(-x)^3 + c*(-x)
–7

f(-x)=-a*x^7 - b*x^3 - c*x
–7

If we calculate the
sum

f(x)+ f(-x)= a*x^7 + b*x^3 + c*x – 7-a*x^7 - b*x^3 -
c*x –7

f(x)+ f(-x)=-14

From
the sum above, we’ve noticed that regardless the value of x, the sum will have always
the same value “-14”.

So the sum is not depending on x. The
conclusion would b that:

f(7)+
f(-7)=-14

But f(7)=7, the value being given in  the
enunciation. So we’ll substitute it in the sum:

7+
f(-7)=-14

f(-7)=-14-7

f(-7)=-21