4. Given the functions f ( x ) = 6 x 2 + 4 x + 6 g ( x ) = 5 x + 2 Compute the f

Question

4. Given the functions

• f(x) = 6x2 + 4x+ 6
• g(x) = 5x + 2

Compute the following (you must simplify each polynomial as far aspossible to receive full credit) Use the ^ (shift-6 on thekeyboard) to enter a power. So to enter x2 + 3x+ 1, you would type x^2 + 3x + 1. f(g(x)) = g(f(x)) = PLEASE ANSWER IN CORRECT FORM. PLEASE ANSWER IN CORRECT FORM. 4. Given the functions

• f(x) = 6x2 + 4x+ 6
• g(x) = 5x + 2

Compute the following (you must simplify each polynomial as far aspossible to receive full credit) Use the ^ (shift-6 on thekeyboard) to enter a power. So to enter x2 + 3x+ 1, you would type x^2 + 3x + 1. f(g(x)) = g(f(x)) = PLEASE ANSWER IN CORRECT FORM.

Explanation / Answer

f ( g ( x ) ) = f ( 5x + 2 ) = 6 ( 5x + 2 )^2 + 4 ( 5x + 2 )+ 6 = 6 ( 25x^2 + 20x + 4 ) + 20x + 8 + 6                                      = 150x^2 + 120x + 24 + 20x + 14                                      = 150x^2 + 140x + 38 g ( f ( x ) ) = g ( 6x^2 + 4x + 6 ) = 5 ( 6x^2 + 4x + 6 ) + 2= 30x^2 + 20x + 30 + 2 = 30x^2 + 20x + 32 hope this helps

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