Express the function h(x)=(x+1)^7 in the form f(g(x)), where f(x)=x^7, find the function g(x). Please help ASAP so confused!!! :(
Well, by the "just look at it" theorem, if g(x) = x+1
and f(x) = x^7
then f(g(x)) = f(x+1) = (x+1)^7 which is given as h(x)
To express the function h(x) = (x+1)^7 in the form f(g(x)), we need to find the function g(x) that will allow us to do so.
Let's break down the given function h(x) = (x+1)^7 step by step:
1. Start with the function f(x) = x^7, which is the final function we want in the form f(g(x)).
2. Notice that the expression (x+1) is raised to the power of 7 in h(x).
3. Therefore, we can consider the function g(x) to be g(x) = x + 1.
g(x) is the "inner" or "inside" function that transforms x into (x+1).
4. Now, if we substitute g(x) into f(x), we get f(g(x)) = (x + 1)^7, which matches the original function h(x).
So, the function g(x) that allows us to express h(x) as f(g(x)) is g(x) = x + 1.
In summary:
h(x) = (x+1)^7 can be expressed as f(g(x)), where f(x) = x^7 and g(x) = x + 1.
I hope this clarifies your confusion!