For these problems, treat each as its own problem, with different meanings for g(x) or f(x) than each other or examples we’ve used previously

Question

f(x)=x^2+4

g(x)=x−1

Find (g+f)(x)

g(x)=4x−1

f(x)=x−2

Find g(x)−f(x)

g(x)=3x+1

h(x)=2x−2

Find (g−h)(x)

g(x)=x^2−2x−1

h(x)=2x−2

Find g(x)+h(x)

Answer 1

f(x)=x²+4

g(x)=x−1

Find (g+f)(x)

(x²+4)+(x−1) Combine like terms

x²+x+3

g(x)=4x−1

f(x)=x−2

Find g(x)−f(x)

(4x−1)-(x−2) Remove the parenthesis by distributing the -1

4x−1-x+2 Combine like terms

3x+1

g(x)=3x+1

h(x)=2x−2

Find (g−h)(x)

(3x+1)-(2x−2) Remove the parenthesis by distributing the -1

3x+1-2x+2 Combine like terms

x+3

g(x)=x^2−2x−1

h(x)=2x−2

Find g(x)+h(x)

(x²−2x−1)+(2x−2) Combine like terms

x²-3