Another Homework Question :)

[MathStudent17314]

Find two functions f and g such that the composition
f ∘ g = h expresses the given correspondence. Several answers are possible.

h(x) = (x − 1)^3

 

[Deleted member 4993]

Find two functions f and g such that the composition
f ∘ g = h expresses the given correspondence. Several answers are possible.

h(x) = (x − 1)^3

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

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Please share your work/thoughts about these problems.

 

[Deleted member 4993]

Find two functions f and g such that the composition
f ∘ g = h expresses the given correspondence. Several answers are possible.

h(x) = (x − 1)^3

I'll give you a different example:

suppose f(x) = x^5 and

g(x) = x - 32

What would be fog?

 

[Steven G]

f(x) = x and g(x) = h(x) OR g(x) = x and f(x) = h(x)

 

[MathStudent17314]

Find two functions f and g such that the composition
f ∘ g = h expresses the given correspondence. Several answers are possible.

h(x) = (x − 1)^3

I am not sure how to input this to find the answer as I was just previously taught by someone on this forum how to do f(x) and g(x). I tried inputting f(x-1)^3 and g(x-1)^3 but it is not giving me the correct answer. This problem is very similar to the one I previously posted but I do not know how to set it up differently.

 

[Steven G]

What are the two steps to compute (x-1)^3 if you were told x. Answer: subtract 1 and then cube (in that order).

So define two functions where one subtracts 1 and the other cubes.

 

[Deleted member 4993]

I am not sure how to input this to find the answer as I was just previously taught by someone on this forum how to do f(x) and g(x). I tried inputting f(x-1)^3 and g(x-1)^3 but it is not giving me the correct answer. This problem is very similar to the one I previously posted but I do not know how to set it up differently.

Did you try to answer the question posed in response #3?

 

[skeeter]

[MATH]h(x) = {\color{red}(} {\color{blue}x-1} {\color{red})^3}[/MATH]
one function inside another function ... a composition of two functions