Express the function h(x)=1/x+5 in the form f(g(x)), where g(x)=(x+5), and
f(x)=
Please help immediately!!!:(
Well, well, well, it seems like you're in quite a hurry. Don't worry, Clown Bot is here to save the day with a dash of humor!
Let's start by understanding the given function h(x) = 1/x + 5. We need to express it in the form f(g(x)), where g(x) = x + 5.
Here's the breakdown with a humorous twist:
Step 1: Let's work on g(x) first. Since g(x) = x + 5, it's like adding five to x, which is easy-peasy lemon squeezy. Imagine you have five apples, and you decide to add them to your basket of x apples. Voila! You end up with x + 5 apples in total. Easy, right?
Step 2: Moving onto f(x). Well, we don't know the exact function for f, so let's call it "mystery function." It's like f(x) is playing hide-and-seek, trying to make our lives more interesting. Oh, you sneaky function!
So, putting it all together in the form f(g(x)): h(x) = f(g(x)) = f(x + 5). Ta-da! We expressed the function h(x) in the requested form.
Remember, math can be fun, even when you're in a hurry!
To express the function h(x) = 1/x + 5 in the form f(g(x)), we need to rewrite the function h(x) as f(g(x)) by finding suitable functions f(x) and g(x).
Let's start by expressing g(x) = (x + 5), as given.
Next, we need to find f(x) such that when we substitute g(x) into f(x), it will give us h(x).
To do this, let's substitute g(x) into f(x) and see if we can simplify it to h(x).
f(g(x)) = f(x + 5)
Now, let's substitute g(x) into f(x):
h(x) = 1/x + 5
We can see that h(x) is the same as f(x + 5), so we can express the function h(x) as f(g(x)):
h(x) = f(x + 5)
Therefore, the function h(x) = 1/x + 5 can be expressed in the form f(g(x)) as f(x + 5).
To express the function h(x) = 1/x + 5 in the form f(g(x)), we need to find a function f(x) such that the composition f(g(x)) produces the same output as h(x).
First, let's look at the function g(x) = (x + 5). This function takes an input x, adds 5 to it, and outputs the result.
Now, we need to find a function f(x) that takes the output of g(x) and produces the same result as h(x).
First, let's find the output of g(x) when the input is x:
g(x) = (x + 5)
Now, let's substitute this result into the function h(x):
h(x) = 1 / (x + 5) + 5
To express h(x) in the form f(g(x)), we need to find a function f(x) such that f(g(x)) = 1 / (x + 5) + 5.
Let's define f(x) = 1 / x. This function takes an input x, finds its reciprocal (1/x), and outputs the result.
Now, if we substitute g(x) into f(x), we have:
f(g(x)) = f(x + 5) = 1 / (x + 5)
Finally, let's substitute this expression back into h(x):
h(x) = 1 / (x + 5) + 5
Therefore, the function h(x) = 1 / x + 5 can be expressed in the form f(g(x)), where g(x) = (x + 5) and f(x) = 1 / x.
f(x) = 1/x
f(g(x)) = 1/g(x) = 1/(x+5)