Question

Please help with 32 and 33, thank you.

Answer 1

Answer:

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