Problem

For $f(x)=7 x$ and $g(x)=-x$, find each of the following
a. $(f+g)(-3)$
b. $(f-g)(-1)$
c. $(f \cdot g)(2)$
d. $\left(\frac{1}{g}\right)(2)$
a. $(f+g)(-3)=-18$ (Simplify your answer)
b. $(f-g)(-1)=-8$ (Simplify your answer)
c. $(1 \cdot g)(2)=-28$ (Simplify your answer)
d. $\left(\frac{1}{g}\right)(2)=\square$ (Simplify your answer)

Answer

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Answer

\(\boxed{-0.5}\)

Steps

Step 1 :\(f(-3) = 7*(-3) = -21\)

Step 2 :\(g(-3) = -(-3) = 3\)

Step 3 :\((f+g)(-3) = f(-3) + g(-3) = -21 + 3 = -18\)

Step 4 :\(\boxed{-18}\)

Step 5 :\(f(-1) = 7*(-1) = -7\)

Step 6 :\(g(-1) = -(-1) = 1\)

Step 7 :\((f-g)(-1) = f(-1) - g(-1) = -7 - 1 = -8\)

Step 8 :\(\boxed{-8}\)

Step 9 :\(f(2) = 7*2 = 14\)

Step 10 :\(g(2) = -(2) = -2\)

Step 11 :\((f \cdot g)(2) = f(2) \cdot g(2) = 14 * -2 = -28\)

Step 12 :\(\boxed{-28}\)

Step 13 :\(g(2) = -(2) = -2\)

Step 14 :\(\left(\frac{1}{g}\right)(2) = \frac{1}{g(2)} = \frac{1}{-2} = -0.5\)

Step 15 :\(\boxed{-0.5}\)

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