Level:
Project ID:
9000007203
Accepted:
1
Clonable:
0
Easy:
0
Consider the function
\[
f(x) =\mathop{ \mathrm{sgn}}\nolimits (x - 2)
\]
defined on \(\mathop{\mathrm{Dom}}(f) =\mathbb{R} ^{-}\). Find
the parameters \(a\)
a \(b\) and
domain of the linear function
\[
g(x) = ax + b
\]
which ensure that \(f\)
and \(g\)
are identical functions.
\[ \]
Hint: The function \(y =\mathop{ \mathrm{sgn}}\nolimits (x)\)
is the sign function. The values of sign function is
\(1\) for each
positive \(x\),
\(- 1\) for each
negative \(x\)
and \(0\) if
\(x = 0\).
\(a = 0\),
\(b = -1\);
\(\mathop{\mathrm{Dom}}(g) =\mathbb{R} ^{-}\)
\(a = 0\),
\(b = 1\);
\(\mathop{\mathrm{Dom}}(g) =\mathbb{R} ^{+}\)
\(a = 1\),
\(b = 0\);
\(\mathop{\mathrm{Dom}}(g) =\mathbb{R} ^{-}\)
\(a = -1\),
\(b = 0\);
\(\mathop{\mathrm{Dom}}(g) =\mathbb{R} ^{+}\)