Solution Found!
If f sxd x 1 s2 2 x and tsud u 1 s2 2 u , is it true that f t?
Chapter 1, Problem 1(choose chapter or problem)
If \(f(x)=x+\sqrt{2-x}\) and \(g(u)=u+\sqrt{2-u}\), is it true that \(f=g\)?
Questions & Answers
QUESTION:
If \(f(x)=x+\sqrt{2-x}\) and \(g(u)=u+\sqrt{2-u}\), is it true that \(f=g\)?
ANSWER:Step 1 of 2
Given functions are
\(f(x)=x+\sqrt{2-x}\)
\(g(u)=u+\sqrt{2-x}\)
For the function \(f(x)\) the domain of definition is the half open half closed interval \((-\infty, 2]\) as \(f(x)\) becomes undefined for \(x>2\).
Again, For the function \(g(u)\), the domain of definition is the half open half closed interval \((-\infty, 2]\) as \(g(u)\) becomes undefined for \(u>2\).
The range of the function \(f(x)\) is the set \(\left\{y \in \mathbb{R}: y \leq \frac{9}{4}\right\}\). The same set is the range for \(g(u)\).
Thus, both the functions have equal domain and range set.