Consider these three function rules: $f ( x ) = 2 x + 1 \quad g ( i n p u t ) = 4 \cdot \text { input } h ( \text { input } ) = ( \text { input } ) ^ { 2 }$
Give the final output if 2 is the input to each of the following combinations.
A) The combination is [first f(x) then g(input)] and then h(output from that combination). In other words, the output of f is the input for g, and the input of that combination is the input for h.
B) The output from f(x) is the input to the combination of g and h [first g(input) then h(input)]. In other words, combine g and h and use this new function to combine with f.
C) What do your results from parts A and B suggest about associativity of combinations of functions? (Note to the instructor: Use this item cautiously, unless you have treated associativity.)

Question

Consider these three function rules: $f ( x ) = 2 x + 1 \quad g ( i n p u t ) = 4 \cdot \text { input } h ( \text { input } ) = ( \text { input } ) ^ { 2 }$ 
Give the final output if 2 is the input to each of the following combinations.
A) The combination is [first f(x) then g(input)] and then h(output from that combination). In other words, the output of f is the input for g, and the input of that combination is the input for h.
B) The output from f(x) is the input to the combination of g and h [first g(input) then h(input)]. In other words, combine g and h and use this new function to combine with f.
C) What do your results from parts A and B suggest about associativity of combinations of functions? (Note to the instructor: Use this item cautiously, unless you have treated associativity.)

Quizplus · Accepted Answer

The Answer of Consider these three function rules: $f ( x ) = 2 x + 1 \quad g ( i n p u t ) = 4 \cdot \text { input } h ( \text { input } ) = ( \text { input } ) ^ { 2 }$ 
Give the final output if 2 is the input to each of the following combinations.
A) The combination is [first f(x) then g(input)] and then h(output from that combination). In other words, the output of f is the input for g, and the input of that combination is the input for h.
B) The output from f(x) is the input to the combination of g and h [first g(input) then h(input)]. In other words, combine g and h and use this new function to combine with f.
C) What do your results from parts A and B suggest about associativity of combinations of functions? (Note to the instructor: Use this item cautiously, unless you have treated associativity.)

Consider These Three Function Rules f(x)=2x+1g(input)=4⋅ input h( input )=( input )2f ( x ) = 2 x + 1 \quad g ( i n p u t ) = 4 \cdot \text { input } h ( \text { input } ) = ( \text { input } ) ^ { 2 }f(x)=2x+1g(input)=4⋅ input h( input )=( input )2

Consider These Three Function Rules $f ( x ) = 2 x + 1 \quad g ( i n p u t ) = 4 \cdot \text { input } h ( \text { input } ) = ( \text { input } ) ^ { 2 }$