Find (gof)(4) when

Question

f(x) = 3x−12 g(x) = 2x^2+7x−11?

Answer 1

Step 1 :

Given functions

f(x) = 3x − 12

g(x) = 2x² + 7x − 11

gof(x) = g [ f(x) ]

g [ 3x − 12 ]

2( 3x − 12 )² + 7 ( 3x − 12 ) − 11

Apply formula : (a-b)²=a²-2ab+b²

2[ (3x)² - 2(3x)(12) + (12)² ] +  21x − 84 − 11

2[ 9x² - 72x + 144 ] +  21x − 84 − 11

18x² - 144x + 288 +  21x − 84 − 11

18x² - 123x + 193

So (gof)(x) = 18x² - 123x + 193

Step 2 :

(gof)(x) = 18x² - 123x + 193

Substitute x = 4

(gof)(4) = 18(4)² - 123(4) + 193

(gof)(4) = -11

Solution :

The solutio is (gof)(4) = -11