Fie functiile f, g : R −→ R, definite prin f (x) = x − 2, g(x) = 2 − x, ∀x ∈ R(a) Sa se calculeze (f ◦ g)(1)

1. Break Down the Problem

We need to calculate the composition of the functions $f$ and $g$, specifically $(f \circ g)(1)$. This means we first need to evaluate $g(1)$ and then substitute this result into the function $f$.

2. Relevant Concepts

• The function $f(x) = x - 2$
• The function $g(x) = 2 - x$
• The composition of functions is defined as $(f \circ g)(x) = f(g(x))$

3. Analysis and Detail

1. Calculate $g(1)$: $g(1) = 2 - 1 = 1$

2. Now substitute this result into $f$: $f(g(1)) = f(1)$ Calculate $f(1)$: $f(1) = 1 - 2 = -1$

4. Verify and Summarize

We calculated $g(1)$ to be $1$, and then $f(1)$ resulted in $-1$. This verifies the steps as consistent with the definitions of the functions.

Final Answer

$(f \circ g)(1) = -1$