i'm having a hard time with composite functions, especially these

Question

Let f (x) = 2x^2 – x – 9 and g(x) = 4x + 1

(a) Find the composite function (f o g)(x) and simplify the results. 



(b) Find (f o g)(-1) .

Answer 1

OK, Jallisca, let's do this thing!

 

Composite functions can be tricky, but let's back up.

 

If I tell you that f(x) = 2x + 5 and ask for f(2), you'd substitute 2 for every x.

 

f(2) = 2(2) + 5 = 9

 

For composite functions, you do the same thing.

 

f(g(x)) = 2(4x + 1)² - (4x + 1) - 9

             = 2( 4x + 1)(4x + 1) - (4x +1) - 9

             = 2(16x² + 8x + 1) - (4x + 1) - 9

             = 32x² + 16x + 2 - 4x - 1 - 9

             = 32x² + 12x - 8

 

There is your composite function! 

 

f(g(-1)) = 32(-1²) + 12(-1) -8

              = 32(1) -12 - 8

              = 12

 

Hope this helps!

 

Answer 2

f(x)=2x²-x-9                g(x)=4x+1

substitute g(x) in for x in the f(x) function

 

(a)

fog(x)=2(4x+1)²-x-9

 

fog(x)=2((4x+1)(4x+1))-x-9

 

fog(x)=2(16x²+8x+1)-x-9

 

fog(x)=32x²+16x+2-x-9

 

fog(x)=32x²+15x-7

 

(b)

substitute -1 for x

fog(-1)=32(-1)²+15(-1)-7

fog((-1)=32-15-7

fog(-1)=10