9000007202
Level:
C
Consider the function
\[
f(x) = [x] + 3
\]
on the domain \(\mathop{\mathrm{Dom}}(f) = (1;2)\).
Find the parameters \(a\)
and \(b\)
and a domain of the linear function
\[
g\colon y = ax + b
\]
which ensure that \(f\)
and \(g\)
are identical functions.
\[ \]
Hint: The function \(y = [x]\)
is a floor function: the largest integer less than or equal to
\(x\). For positive
\(x\) it is also called the
integer part of \(x\).
\(a = 0\),
\(b = 4\);
\(\mathop{\mathrm{Dom}}(g) = (1;2)\)
\(a = 0\),
\(b = 3\);
\(\mathop{\mathrm{Dom}}(g) = (1;2)\)
\(a = 3\),
\(b = 0\);
\(\mathop{\mathrm{Dom}}(g) = (1;2)\)
\(a = -3\),
\(b = 0\);
\(\mathop{\mathrm{Dom}}(g) = (1;2)\)
