F(x) and g(x) such that h(x)=(f•g)(x) h(x)=(5-3x). Suppose that g(x)= 5-3x what is f(x)

Answer 1

Answering this question requires the assumption that your function is in a polynomial form or can be represented as such. This simplifies the problem considerably as it reduces the number of functions you need to consider. You don't need to consider Trig functions, Logarithms, or Exponents.

We start by looking if we notice a pattern between the two functions. We know that g(x) = 5-3x and we know h(x) = 5-3x! In other words, they are the same! This means that whatever function f(x) is needed to not do anything to g(x). There is only 1 function that when multiplied gives the same output and that is f(x) = 1! We know this because 1 multiplied by anything is itself. So for the problem f(x) = 1

To cover my bases you could also mean (f o g)(x) so let's cover that one too. We can solve this by thinking about what function's output is the same as the input because (f o g)(x) means use g(x) as the input for f(x) or in other words f(g(x)). This means that we need a function that has the same input as output. because g(x) is the same as h(x). g(x) is the input and h(x) is the output. The only function with the same input as output is the simple linear function f(x) = x. So in this case f(x) = x.

I hope this helps you!