Referenced from lesson Function Composition (Spring, 2021)

f :: Number -> Number
Consumes a number, multiplies by 3 to produce the result
 
g :: Number -> Number
Consumes a number, adds six to produce the result
 
h :: Number -> Number
Consumes a number, subtracts one to produce the result

fx = 3x

gx = x + 6

hx = x - 1

For each function composition diagrammed below, translate it into the equivalent Circle of Evaluation for Order of Operations. Then write expressions for both versions of the Circles of Evaluation, and evaluate them for x = 4. The first one has been completed for you.

Function Composition Order of Operations Translate & Evaluate

1

h
g
f
x
(h (g (f x)))

-
+
*
3x
6
1
(- (+ (* 3 x) 6) 1)

Composition:

h​(​g​(​f​(​x​)​)​)

Operations:

(​(​3 * x​) + 6​) - 1

Evaluate for x = 4

h(g(f4)) = 17

2

g
f
h
x
(g (f (h x)))

Composition:

Operations:

Evaluate for x = 4

3

h
f
g
x
(h (f (g x)))

Composition:

Operations:

Evaluate for x = 4

4

f
h
g
x
(f (h (g x)))

Composition:

Operations:

Evaluate for x = 4

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