Write the composite function in the form f(g(x)). [Identify the inner function

u = g(x) and the outer function y = f(u).] (Use non-identity functions for f(u) and g(x)).

y = tan(x^5)

(f(u),g(x))=(?)

I thought the answer would be (tan(x),x^5) but it turns out it isn't? I would appericiate it if someone could tell me the right answer or explain how to get it.

g(x) = x^5

f(x) = tan(x)
f(g(x)) = tan(g(x) = tan(x^5)

your answer is correct, but that's not what they asked. They want
f(u) = tan(u)
g(x) = x^5
so, (tan(u),x^5)

Well, well, well, looks like we've got ourselves a composite function puzzle. Don't worry, I'll help you unravel this one!

First things first, let's identify our functions here:

The inner function u = g(x) is the function that takes x and transforms it into our lovely u. In this case, g(x) = x^5. So, we've got one part down!

Now, let's move on to the outer function y = f(u). And in our case, y = tan(x^5). Notice how tan is applied to the whole shebang x^5. So, we can break this down as f(u) = tan(u).

Putting it all together, we have (f(u), g(x)) = (tan(u), x^5), or in other words, y = tan(g(x)).

I hope that clears things up for you! If you need any more assistance, or just want to hear another silly joke, feel free to ask!

To find the composite function in the form f(g(x)), we need to identify the inner function g(x) and the outer function f(u).

In this case, the given function is y = tan(x^5).

To identify the inner function, we look for the function inside another function. In this case, x^5 is inside the tangent function. So, the inner function is g(x) = x^5.

Now, to identify the outer function, we simply look at the remaining part of the given function. In this case, it is y = tan(u). So, the outer function is f(u) = tan(u).

Therefore, the composite function in the form f(g(x)) is:

(f(u),g(x)) = (tan(u), x^5).

To identify the inner and outer functions and form the composite function in the given equation y = tan(x^5), we can follow these steps:

1. Identify the inner function, denoted as u = g(x). In this case, the inner function is u = x^5.

2. Identify the outer function, denoted as y = f(u). In this case, the outer function is y = tan(u).

3. Re-write the composite function in the form f(g(x)). Substitute the inner function u = g(x) into the outer function y = f(u):

f(g(x)) = f(x^5).

Therefore, the correct answer is (f(u), g(x)) = (tan(u), x^5), which is equivalent to (tan(x^5), x^5).

Ah, thanks so much for answering! Can't believe I didn't notice that.

🧞‍♀️