let f(x) =4x^2-6

Question

Let f(x)=4x²-6 and g(x)=x-2

a) Find the composite function (f o g)(x) and simplify it (show work)

b) Find (f o g) (-1). Show work 

Answer 1

a)   (f o g)(x) means f(g(x))

so what you do is substitute g(x) into f(x) for x

(f o g)(x) = f(g(x)) = 4[g(x)]²-6 = 4[x-2]² - 6 = 4[x²-4x+4] -6

= 4x² - 16x + 16 -6 = 4x² - 16x + 10

 

for b)  (f o g) (-1) means evaluate  (f o g)  for x = -1

so (f o g) (-1) = 4x² - 16x + 10  where x = -1

I think you can substitute in the -1 and take it from there.

If not, let us know where you got stuck.

Answer 2

Let f(x)=4x²-6 and g(x)=x-2

a) Find the composite function (f o g)(x) and simplify it (show work)

 

To find the composite function (f o g)(x), simply replace the x in f(x) with g(x):

 

(f o g)(x) = 4g(x)² - 6

 

(f o g)(x) = 4(x-2)² - 6

 

Can you finish it from here?

 

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

 

To find (f o g)(-1), simply plug x = -1 into (f o g)