Find (f•g) (x) and (g•f) (x)
1. f (x) = x+3 , g(x) = x-3
2. f (x) = x⁴ , g(x) = ⁴√x
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Find (f•g) (x) and (g•f) (x)
1. f (x) = x+3 , g(x) = x-3
2. f (x) = x⁴ , g(x) = ⁴√x
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Answer:
Step-by-step explanation:
Sure, I can help you with that!
Let's start with the first question:
(f•g) (x) is the composition of f(x) and g(x), which means that we evaluate the function f(x) first, and then we use the result of that as the input to the function g(x). So the first step is to find f(x) and g(x):
* f(x) = x+3
* g(x) = x-3
Therefore, the composition of f and g is:
(f•g) (x) = g(f(x)) = g(x+3)
Then we just need to find the output for this function:
* (f•g) (x) = g(x+3)
* (f•g) (x) = (x+3)-3
* (f•g/) (x) = x
So the result of the composition of f and g is the function that maps x to x, and is, therefore, the identity function!
Now let's do the second question:
Same process as before:
(g•f) (x) is the composition of g(x) and f(x), which means that we evaluate the function g(x) first, and then we use the result of that as the input to the function f(x).
* f(x) = x⁸
* g(x) = ⁴√x
Therefore, the composition of f and g is:
(g•f) (x) = f(g(x)) = f(¼√x)
And again we just need to find the output for this function:
* (g•f) (x) = f(¼√x)
* (g•f) (x) = x⁴
* (g•f) (x) = (¼√x)⁴
* (g•f) (x) = x¹⁶
And there you have it, the composition of f and g is the function that maps x to x¹⁶!
Answer:
To find (f•g)(x) and (g•f)(x) for the given functions, you'll need to perform the operations of function composition. Here are the results for the two sets of functions:
1. For f(x) = x + 3 and g(x) = x - 3:
(f•g)(x) = f(g(x)) = (x - 3) + 3 = x
(g•f)(x) = g(f(x)) = (x + 3) - 3 = x
So, in this case, (f•g)(x) and (g•f)(x) both simplify to x.
2. For f(x) = x⁴ and g(x) = ∛x (the fourth power and cube root):
(f•g)(x) = f(g(x)) = (∛x)⁴ = x
(g•f)(x) = g(f(x)) = (∛x)⁴ = x
Again, in this case, (f•g)(x) and (g•f)(x) both simplify to x.
So, for both sets of functions, the composition of the functions results in the same value, which is x.
Step-by-step explanation:
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