Answer to Question #105493 in Calculus for khushi

Question

State whether the following statements are true or false. Justify yourself with the help of a short proof or a counter example. (4) The function f:R®R, defined by f(x) =x|x|, is an odd function. (5) The domain of the function f(g(x)), where f(x) =√x and g(x) =√2-x, is [-infinite,2.

Answer 1

4) TRUE

let's find f(-x)=-x|-x|=-x|x|=-f(x), which means that f(x) is an odd function.

5) TRUE

f(g(x))=$\sqrt{\sqrt{2-x}}$ , so the domain is when $2-x \geq 0$ and $x \leq 2$