Question

Write a rule for g(x) = f(-x)-5 when f(x) = x^3 + x^2 -1

Answer 1

If f(x) = x^3 + x^2 - 1, then

f(-x) = (-x)^3 + (-x)^2 - 1

f(-x) = (-1)^3 * x^3 + (-1)^2 * x^2 - 1

f(-x) = (-1) * x^3 + 1 * x^2 - 1

f(-x) = -x^3 + x^2 - 1


So,

g(x) = f(-x) - 5

g(x) = -x^3 + x^2 - 1 - 5

g(x) = -x^3 + x^2 - 6 <----- this is the answer


I hope this helps. =)