Please help with 32 and 33, thank you.

32. ∛((x-7)/4) = f^(-1)(x)

33. -10x - 9

Step-by-step explanation:

32. We want to switch f(x) and x, and then solve for f(x) to get the inverse.

x = 4f(x)³ + 7

subtract 7 from both sides

x -7 = 4f(x)³

divide both sides by 4

(x-7)/4 = f(x)³

cube root both sides

∛((x-7)/4) = f(x)

make f(x) f^(-1)(x) because this is now the inverse

∛((x-7)/4) = f^(-1)(x)

the second answer is correct

33. for composition, we can treat (f · g) (x) as attached picture (content filter!), so we plug g(x) into f(x). This results in

2(-5x-7) + 5

expand

-10x - 14 + 5

add

-10x - 9

the second answer is correct

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