MaizleyJ505761 MaizleyJ505761
  • 25-10-2022
  • Mathematics
contestada

Given the definitions of f(x) and g(x) below, find the value of (gof)(9). f(x) = -x + 11 g(x) = 3x2 - x + 14

Respuesta :

KamoraC399830 KamoraC399830
  • 25-10-2022

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

f(x) = -x + 11

g(x) = 3x² - x + 14​

(gof)(9) = ?

Step 02:

(gof)(x) = 3(-x+11)² - (-x+11) + 14​

= 3(x² + 2(-x)(11) + 121) + x - 11 + 14

= 3(x² - 22x + 121) + x - 11 + 14

= 3x² - 66x + 363 + x - 11 + 14

= 3x² - 65x + 366

(gof)(9) = 3(9)² - 65(9) + 366

= 3(81) - 585 + 366

= 243 - 585 + 366

= 24

The answer is:

(gof)(9) = 24

Answer Link

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