The function g(x) is obtained by substituting x+5 into the function f(x), resulting in g(x) = f(x + 5) = -x - 2.
Step-by-step explanation:
Understanding Function Composition
Let's take a closer look at the given functions f(x) = -x + 3 and g(x) = f(x + 5). To find the expression for g(x), we need to substitute x + 5 into the function f in place of x. Therefore, g(x) becomes:
g(x) = f(x + 5) = - (x + 5) + 3 = -x - 5 + 3 = -x - 2
This step-by-step process shows us how to handle function composition, where one function is applied to the result of another function. In our case, g(x) is the result of applying f to (x + 5), and we used the rules of algebraic operations to find the simplified form of g(x).
The probbable question can be: Find the simplified form of g(x) : f(x)=-x+3;g(x)=f(x+5)