Algebra - Combining Functions (Assignment Problems)

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Section 3.6 : Combining Functions

Given f(x)=x+12 and g(x)=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. $\displaystyle \frac{f}{g}$
Given h(w)=w2−4w and f(w)=2+w2 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. $\displaystyle \left( {\frac{h}{f}} \right)\left( w \right)$
Given A(x)=6x−1 and P(x)=14−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. $\displaystyle \left( {\frac{A}{P}} \right)\left( x \right)$
Given f(t)=2t+9 and g(t)=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. $\left( {g \circ g} \right)\left( t \right)$
Given h(x)=x2+1 and g(x)=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. $\left( {h \circ h} \right)\left( x \right)$
Given A(w)=2w2+9 and R(w)=1−2w−w2 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. $\left( {A \circ A} \right)\left( w \right)$
Given f(x)=9x2+10x+12 and g(x)=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. $\left( {g \circ g} \right)\left( x \right)$
Given g(t)=t+1 and h(t)=2t−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. $\left( {h \circ h} \right)\left( x \right)$
Given f(x)=12x−3 and g(x)=2x+6, t≥0 compute each of the following.
1. $\left( {f \circ g} \right)\left( x \right)$
2. $\left( {g \circ f} \right)\left( x \right)$
Given h(w)=1w−3 and f(w)=1+3ww compute each of the following.
1. $\left( {h \circ f} \right)\left( w \right)$
2. $\left( {f \circ h} \right)\left( w \right)$