If f(x)=4x3+3x2−5x+20 and g(x)=9x3−4x2+10x−55, what is (g−f)(x)?

A) 5x3−7x2+15x−75
B) 5x3+x2+5x+35
C) 13x3−x2+5x−35
D) −5x3+7x2−15x+75

Step-by-step explanation:

(g-f)(x) = 9x³ - 4x² + 10x - 55 - [ 4x³ +3x² - 5x + 20]

To remove the parenthesis, take - inside, multiply f(x) by -1

= 9x³ - 4x² + 10x - 55 -  4x³ - 3x² + 5x - 20  

Now, bring like terms together,

= 9x³ - 4x³ - 4x² - 3x² + 10x + 5x - 55 - 20

= 5x³ - 7x² + 15x - 75

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2

i pretty sure it is