Consider the functions f , g : R → R defined as f (x) = 3px + 1 and g(x) = x3. Find theformulas for g ◦ f and f ◦ g

Question

Consider the functions f , g : R → R defined as f (x) = 3px + 1 and g(x) = x3. Find theformulas for g ◦ f and f ◦ g
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Solution 1

To find the formulas for g ◦ f and f ◦ g, we need to substitute the function g into f and vice versa.

First, let's find the formula for g ◦ f. To do this, we substitute f(x) into g(x):

g ◦ f(x) = g(f(x))

Substituting f(x) = 3px + 1 into g(x), we get:

g ◦ f(x) = (3px + 1)^3

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