Question

Given f(x)= 1 - 5x and g(x) = (1 - x). find (f ∘ g )(x). (the composition of f and g)

Answer 1

The composition (f \circ g)(x) is found by substituting g(x) into f(x) and simplifying. For the functions f(x)= 1 - 5x and g(x) = (1 - x), the composition (f \circ g)(x) equals -4 + 5x after simplifying the expressions.

Step-by-step explanation:

The question asks how to find the composition of two functions, which is a concept in mathematics where one function is applied to the result of another function. In this case, the functions are f(x)= 1 - 5x and g(x) = (1 - x). To find this, we substitute g(x) into f(x) wherever there is an x.

Here's the step-by-step process:

1. Write down f(x) replacing x with g(x). This will look like f(g(x)) = 1 - 5(1 - x).
2. Simplify the expression inside the parentheses: 1 - 5(1 - x) = 1 - 5 + 5x.
3. Further simplify by combining like terms: 1 - 5 + 5x = -4 + 5x.
4. Therefore, the composition of the function is equals -4 + 5x.