If f(x)=√(|x-1|) and g(x)=sinx, then (f o g)(x)= (a) sin√(|x-1|) (b) |sinx / 2-cosx / 2| (c) sin

step 1 Hi guys, so we have this problem in which we need to find out the fx. That is what a square root

If f(x)=√(|x-1|) and g(x)=sinx, then (f o g)(x)= (a)...

Key Concepts

Trigonometric Functions

Trigonometric functions, such as the sine function, are fundamental in the study of periodic phenomena. The sine function, often denoted by sin x, maps an angle (or real number) to its sine value and is used extensively in geometry, physics, and engineering to model waves, rotations, and oscillations.

Absolute Value Function

The absolute value function, denoted as |x|, outputs the non-negative value of its input regardless of its sign. It is used to measure the magnitude of a real number and appears frequently in mathematical expressions to ensure non-negativity, particularly when combined with other functions such as the square root.

Function Composition

Function composition is the process of applying one function to the result of another. It involves taking the output produced by one function and using it as the input to a second function, denoted as (f ? g)(x) = f(g(x)). This concept is fundamental in mathematics as it allows complex functions to be built from simpler ones and is used in various problem-solving contexts.

Square Root Function

The square root function, typically written as ?x, assigns to each non-negative input the unique non-negative number whose square is the input. It is an important operation in algebra and calculus and requires that the expression inside the square root is non-negative, often influencing the domain of the overall function.

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