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Section 3.6 : Combining Functions

1. Given \(f\left( x \right) = 6x + 2\) and \(g\left( x \right) = 10 - 7x\) compute each of the following.
   1. \(\left( {f - g} \right)\left( 2 \right)\)
   2. \(\left( {g - f} \right)\left( 2 \right)\)
   3. \(f\,g\)
   4. \(\displaystyle \left( {\frac{f}{g}} \right)\left( x \right)\)
   Solution
2. Given \(P\left( t \right) = 4{t^2} + 3t - 1\) and \(A\left( t \right) = 2 - {t^2}\) compute each of the following.
   1. \(\left( {P + A} \right)\left( t \right)\)
   2. \(A - P\)
   3. \(\left( {PA} \right)\left( t \right)\)
   4. \(\displaystyle \left( {\frac{P}{A}} \right)\left( { - 2} \right)\)
   Solution
3. Given \(h\left( z \right) = 7z + 6\) and \(f\left( z \right) = 4 - z\) compute each of the following.
   1. \(\left( {f\,h} \right)\left( z \right)\)
   2. \(\left( {f \circ h} \right)\left( z \right)\)
   3. \(\left( {h \circ f} \right)\left( z \right)\)
   4. \(\left( {h \circ h} \right)\left( z \right)\)
   Solution
4. Given \(f\left( x \right) = 6{x^2}\) and \(g\left( x \right) = {x^2} + 3x - 1\) compute each of the following.
   1. \(\left( {g\,f} \right)\left( x \right)\)
   2. \(\left( {f \circ g} \right)\left( x \right)\)
   3. \(\left( {g \circ f} \right)\left( x \right)\)
   4. \(\left( {f \circ f} \right)\left( x \right)\)
   Solution
5. Given \(R\left( t \right) = \sqrt t - 2\) and \(A\left( t \right) = {\left( {t + 2} \right)^2}\), \(t \ge 0\) compute each of the following.
   1. \(\left( {R \circ A} \right)\left( t \right)\)
   2. \(\left( {A \circ R} \right)\left( t \right)\)
   Solution