Write a rule for G

Question

write a rule for g: f(x)=x^5-2x+3, g(x)=-f(x)+1

Answer 1

Negative f(x) is -(x⁵ - 2x + 3) = -x⁵ + 2x - 3

Negative f(x) + 1 is -x⁵ + 2x - 3 + 1 which is -x⁵ + 2x - 2 so:

g(x) = -x⁵ + 2x - 2

Answer 2

if g(x) is -f(x) + 1, we can take f(x), multiply it by -1, and then add one to the result:

f(x) = x⁵ - 2x + 3

-f(x) = -x⁵ + 2x - 3

-f(x) + 1 = -x⁵ + 2x - 2 = g(x)