# Task 3. 15 points

Solve the inequality

$f(g(x))>g(f(x))$, if $f(x)=\left\{\begin{array}{cc}x, & x \geq 0 \\ 0, & x<0\end{array} ; g(x)=\left\{\begin{array}{cc}2-x, & x<2 \\ 0, & x \geq 2\end{array}\right.\right.$.

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# Solution

![](https://cdn.mathpix.com/cropped/2024_05_06_af6c9b4d3aae602586a7g-03.jpg?height=149&width=1156&top_left_y=565&top_left_x=290)

$f(g(x)) > g(f(x))$ for $x < 0$.

Answer: $x < 0$.

## Criteria:

Correct solution and correct answer provided - 15 points.

Correctly found functions $f(g(x))$ and $g(f(x))$, but the inequality is solved incorrectly - 10 points.

One of the functions $f(g(x))$ and $g(f(x))$ is found correctly, the other incorrectly - 5 points.

Correct answer provided without a solution - 1 point.

In all other cases - 0 points.