Algebra - Combining Functions (Practice Problems)

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Section 3.6 : Combining Functions

Given f(x)=6x+2 and g(x)=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
Given P(t)=4t2+3t−1 and A(t)=2−t2 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
Given h(z)=7z+6 and f(z)=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
Given f(x)=6x2 and g(x)=x2+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
Given R(t)=√t−2 and A(t)=(t+2)2, t≥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