chlo9679
contestada

20 points!!! Will mark brainlist to whoever gives me the correct answers with the work:)

Use the information below for Part A, Part B, and Part C.

f(x) = 1/2x -7

g(x) = 2x + 14

Part A: Find (fog)(x). Show your work.

Part B: Find (gºf)(x). Show your work.

Part C: Use your answers to Part A and Part B to determine whether the two functions are inverses. Explain your answer fully.

Respuesta :

jesusm1

Answer:

  1. (1/2(2x+14)-7) = 1x+7-7= x
  2. g(f(x))= 2(1/2x-7)+14= x-14+14= x
  3. We have the result being two variables of linearity hence they are not inverses. In order to be inverses they should have had switched notations, ie: -x vs x

sqdancefan

9514 1404 393

Answer:

  A:  (f∘g)(x) = x

  B:  (g∘f)(x) = x

  C:  the functions are inverses

Step-by-step explanation:

A: (f∘g)(x) = f(g(x)) = f(2x +14)

  = 1/2(2x +14) -7 = x +7 -7 = x

  (f∘g)(x) = x

__

B: (g∘f)(x) = g(f(x)) = g(1/2x -7)

  = 2(1/2x -7) +14 = x -14 +14 = x

  (g∘f)(x) = x

__

C: When a function is operated on by its inverse, then original argument value is restored. That is the case for functions f and g, so the two functions are inverses.