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Find the following functions and show all work

Find the following functions and show all work-example-1

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The values are : f(g(x)) = 16√2 + 23, where g(x) is plugged into f(x). g(f(x)) = 25^6, where f(x) is plugged into g(x).

Both depend on the input value!

We are asked to find the following functions:

f(g(x)) and g(f(x))

where f(x) = √2x + 23 and g(x) = x^6.

To find f(g(x)), we first need to find the value of g(x). Then we plug that value into f(x).

g(x) = x^6, so g(2) = 2^6 = 64.

Now we know that g(2) = 64. Let's plug that into f(x):

f(g(x)) = f(64) = √2(64) + 23 = 16√2 + 23

Therefore, f(g(x)) = 16√2 + 23.

To find g(f(x)), we need to find the value of f(x). Then we plug that value into g(x).

f(x) = √2x + 23, so f(2) = √2(2) + 23 = 25.

Now we know that f(2) = 25. Let's plug that into g(x):

g(f(x)) = g(25) = 25^6.

Therefore, g(f(x)) = 25^6.

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