Please I need help with my math homework quickly please

Question

Question 1: Use composition to identify the functions that are inverses of each other.

 

 A.)

 

 B.)

 

 C.)

 D.)

 

 

 

Question 2: Identify the inverse of f(x) = 4 + x2. Determine whether it is a function and state its domain and range.

 

A.) 

 

 

B.)

 

 

 C.)

 

 

D.) 

 

help

Answer 1

Answer 2

If functions are inverses of each other then f(g(x)) = x and g(f(x)) = x

For A), f(g(x)) = (√(x-1))² - 1 = (x - 1) - 1 = x - 2 therefore these are not inverse functions.

For B), f(g(x)) = (√(x-1))² + 1 = (x - 1) + 1 = x and g(f(x)) = √((x²+1) - 1) = √x² = x therefore these are inverse functions.

I'll let you use the same process for C and D.

For problem 2), if f(x) = 4 + x² to find the inverse, first replace f(x) with "y" then switch the places of the "x" and "y":

y = 4 + x²

x = 4 + y² now solve for "y":

y² = x = 4

y = ±√(x - 4)

Then replace the "y" with f^-1(x):

f^-1(x) = ±√(x - 4)

Since you cannot take the square root of a negative number (in the real number system), then x - 4 > 0 or x > 4