Answer to Question #170467 in Algebra for Briana Hetrick

Question

Let f(x)=2−x and g(x)=x3-2, find:

a.(f∘g)(0)=

b. (g∘f)(0)=

c. (f∘g)(x)=

     

d. (g∘f)(x)=

Answer 1

a.

$$(f\circ g)(x)=2-(x^3-2)=4-x^3$$

$$(f\circ g)(0)=4-(0)^3=4$$

b.

$$(g\circ f)(x)=(2-x)^3-2$$

$$(g\circ f)(0)=(2-0)^3-2=6$$

c.

$$(f\circ g)(x)=2-(x^3-2)=4-x^3$$

g.

$$(g\circ f)(x)=(2-x)^3-2$$