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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