Question

III. Let g(x) = 4x + 1 represent the conversion from spots to stars. Let h(x) = x2 - 2 represent the conversion from stars to asteroids. Create a composite function that converts spots directly to asteroids.

Answer 1

g(x) = 4x + 1
h(x) = x^2 - 2
(g o h)(x) = g(h(x)) = g(x^2 - 2) = 4(x^2 - 2) + 1 = 4x^2 - 8 + 1 = 4x^2 - 7

Answer 2

g ( x ) = 4 x + 1 ( spots → stars )
h ( x ) = x² - 2 ( stars → asteroids )
Composite function:
h ( g ( x ) ) = ( 4 x + 1 )² - 2 =
= 16 x² + 8 x + 1 - 2 =
= 16 x² + 8 x - 1 ( spots → asteroids )