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Home / Algebra / Graphing and Functions / Combining Functions
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Section 3-6 : Combining Functions

1. Given $$f\left( x \right) = x + 12$$ and $$g\left( x \right) = 9 + 4x$$ compute each of the following.
1. $$f + g$$
2. $$\left( {f - g} \right)\left( 1 \right)$$
3. $$\left( {f\,g} \right)\left( x \right)$$
4. $$\displaystyle \frac{f}{g}$$
2. Given $$h\left( w \right) = {w^2} - 4w$$ and $$f\left( w \right) = 2 + {w^2}$$ compute each of the following.
1. $$\left( {h - f} \right)\left( w \right)$$
2. $$\left( {f + h} \right)\left( { - 4} \right)$$
3. $$f\,h$$
4. $$\displaystyle \left( {\frac{h}{f}} \right)\left( w \right)$$
3. Given $$A\left( x \right) = 6x - 1$$ and $$\displaystyle P\left( x \right) = \frac{1}{{4 - x}}$$ compute each of the following.
1. $$\left( {A + P} \right)\left( 0 \right)$$
2. $$\left( {P - A} \right)\left( { - 2} \right)$$
3. $$AP$$
4. $$\displaystyle \left( {\frac{A}{P}} \right)\left( x \right)$$
4. Given $$f\left( t \right) = 2t + 9$$ and $$g\left( t \right) = 2t - 1$$ compute each of the following.
1. $$\left( {f\,g} \right)\left( t \right)$$
2. $$\left( {f \circ g} \right)\left( t \right)$$
3. $$\left( {g \circ f} \right)\left( t \right)$$
4. $$\left( {g \circ g} \right)\left( t \right)$$
5. Given $$h\left( x \right) = {x^2} + 1$$ and $$g\left( x \right) = 6 - 4x$$ compute each of the following.
1. $$\left( {g\,h} \right)\left( x \right)$$
2. $$\left( {g \circ h} \right)\left( x \right)$$
3. $$\left( {h \circ g} \right)\left( x \right)$$
4. $$\left( {h \circ h} \right)\left( x \right)$$
6. Given $$A\left( w \right) = 2{w^2} + 9$$ and $$R\left( w \right) = 1 - 2w - {w^2}$$ compute each of the following.
1. $$\left( {A\,R} \right)\left( w \right)$$
2. $$\left( {A \circ R} \right)\left( w \right)$$
3. $$\left( {R \circ A} \right)\left( w \right)$$
4. $$\left( {A \circ A} \right)\left( w \right)$$
7. Given $$f\left( x \right) = 9{x^2} + 10x + 12$$ and $$g\left( x \right) = 2$$ compute each of the following.
1. $$\left( {f\,g} \right)\left( x \right)$$
2. $$\left( {g \circ f} \right)\left( x \right)$$
3. $$\left( {f \circ g} \right)\left( x \right)$$
4. $$\left( {g \circ g} \right)\left( x \right)$$
8. Given $$g\left( t \right) = t + 1$$ and $$\displaystyle h\left( t \right) = \frac{2}{{t - 3}}$$ compute each of the following.
1. $$\left( {g\,h} \right)\left( t \right)$$
2. $$\left( {g \circ h} \right)\left( t \right)$$
3. $$\left( {h \circ g} \right)\left( t \right)$$
4. $$\left( {h \circ h} \right)\left( x \right)$$
9. Given $$\displaystyle f\left( x \right) = \frac{1}{2}x - 3$$ and $$g\left( x \right) = 2x + 6$$, $$t \ge 0$$ compute each of the following.
1. $$\left( {f \circ g} \right)\left( x \right)$$
2. $$\left( {g \circ f} \right)\left( x \right)$$
10. Given $$\displaystyle h\left( w \right) = \frac{1}{{w - 3}}$$ and $$\displaystyle f\left( w \right) = \frac{{1 + 3w}}{w}$$ compute each of the following.
1. $$\left( {h \circ f} \right)\left( w \right)$$
2. $$\left( {f \circ h} \right)\left( w \right)$$
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