Chapter 1: Q81E (page 7)
Find the domain and range of the function
\(g\left( x \right) = {\sin ^{ - 1}}\left( {3x + 1} \right)\)
The domain and range of the function are \(\left[ { - \frac{2}{3},0} \right]\) and \(\left[ { - \frac{\pi }{2},\frac{\pi }{2}} \right]\).
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Sketch the graph of the function
\(f\left( x \right) = \frac{{\left| x \right|}}{x}\)
If f and g are both even functions, is fg even? If f and g are both odd functions, is fg odd? What if f is even and g is odd? Justify your answers.
Find the domain and range and sketch the graph of the function \(h\left( x \right) = \sqrt {4 - {x^2}} \).
If \(f\left( x \right) = 3{x^2} - x + 2\), find \(f\left( 2 \right)\), \(f\left( { - 2} \right)\), \(f\left( a \right)\), \(f\left( { - a} \right)\), \(f\left( {a + 1} \right)\), \(2f\left( a \right)\), \(f\left( {2a} \right)\), \(f\left( {{a^2}} \right)\), \({\left( {f\left( a \right)} \right)^2}\) and \(f\left( {a + h} \right)\).
Find the domain of the function.
6. \(g\left( x \right) = \frac{{\bf{1}}}{{1 - tanx}}\)
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