Question

Evaluate (g∘f)(x)(g∘f)(x) where f(x)=1f(x)=1 and . Explain whether this evaluation is possible and why or not.

Answer 1

To evaluate (g∘f)(x)(g∘f)(x), substitute the function f(x)=1 into g(x) and then substitute the result back into g(x) again. The evaluation is 1.

Step-by-step explanation:

To evaluate (g∘f)(x)(g∘f)(x), we first need to understand the concept of function composition. Function composition involves using the output of one function as the input for another function. In this case, we have f(x)=1 and g(x)=x. To evaluate (g∘f)(x)(g∘f)(x), we substitute the function f(x)=1 into the function g(x) and then substitute the result back into the function g(x) again.

First, substitute f(x)=1 into g(x). g(f(x))=g(1)=1.

Next, substitute the result g(f(x))=1 back into g(x). g(g(f(x)))=g(1)=1.

Therefore, the evaluation of (g∘f)(x)(g∘f)(x) is 1.