0. Functions

Find functions ƒand g such that ƒ(g(x)) = (x² +1)⁵ . Find a different pair of functions ƒ and g that also satisfy ƒ(g(x)) = (x² +1)⁵  

Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>

a. (ƒ o g ) (2)

Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>

b. g (ƒ (2))

Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>

c. ƒ(g (4))

Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>

d. g(ƒ(5))

Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>

e. ƒ(ƒ(8))

Use the table to evaluate the given compositions. <IMAGE>

g(ƒ(4))

Use the table to evaluate the given compositions. <IMAGE>

g(h(ƒ(4)))

Use the table to evaluate the given compositions. <IMAGE>

h(h(h(0)))

Use the table to evaluate the given compositions. <IMAGE>

g(ƒ(h(4)))

Use the table to evaluate the given compositions. <IMAGE>

ƒ(ƒ(h(3)))

Suppose ƒ is an even function with ƒ(2) = 2 and g is an odd function with g(2) = -2. Evaluate ƒ(-2) , ƒ(g(2)), and g(ƒ(-2))

Composite functions and notation

Let ƒ(x)= x² - 4 , g(x) = x³ and F(x) = 1/(x-3). Simplify or evaluate the following expressions.

g(1/z)

Composite functions and notation

Let ƒ(x)= x² - 4 , g(x) = x³ and F(x) = 1/(x-3).

Simplify or evaluate the following expressions.

F(y⁴)

Composite functions and notation

Let ƒ(x)= x² - 4 , g(x) = x³ and F(x) = 1/(x-3).

Simplify or evaluate the following expressions.

F(g(y))