Question

Show the composition of functions for f (8 (x)) using the following functions f (x) = 3x² + 2x + 1 and g(x) = x²-4

composition.
O f(8(x)) = 3(8(x))² + 2(8(x)) + 1
O f(8(x)) = 3(8)² + 2(8) + 1
O f(8(x)) = 3(64x²) + 16x + 1
O f(8(x)) = 3(64) + 2(8) + 1"

Answer 1

The correct composition of functions f(g(x)) with f(x) = 3x² + 2x + 1 and g(x) = 8x is f(g(x)) = 3(64x²) + 16x + 1.

Step-by-step explanation:

To show the composition of functions for f(g(x)) using the functions f(x) = 3x² + 2x + 1 and g(x) = 8(x), we substitute g(x) into f(x). Here, g(x) simply represents the multiplication of the variable x by 8, so we replace every instance of x in f(x) with 8x. The correct composition is:

f(g(x)) = f(8(x)) = 3(8x)² + 2(8x) + 1

Then, we simplify the equation by squaring the term (8x), which is 64x², and multiplying 3 by 64x² and 2 by 8x:

f(g(x)) = 3(64x²) + 16x + 1 = 192x² + 16x + 1

So, the correct answer is 3(64x²) + 16x + 1.