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College Algebra

Exercises 4.3 Practice Problems

1.

Suppose \(f(x) = 2x+1\text{.}\)
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Evaluate each of the following:
  1. \(\displaystyle f^{-1}(0)\)
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  2. \(\displaystyle f^{-1}(4)\)
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  3. \(\displaystyle f^{-1}(9)\)
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  4. \(\displaystyle f^{-1}(1)\)
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  5. \(\displaystyle f^{-1}(10)\)
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Answer.
  1. \(\displaystyle f^{-1}(0)=\frac{-1}{2}\)
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  2. \(\displaystyle f^{-1}(4)=\frac{3}{2}\)
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  3. \(\displaystyle f^{-1}(9)=4\)
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  4. \(\displaystyle f^{-1}(1)=0\)
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  5. \(\displaystyle f^{-1}(10)=\frac{9}{2}\)
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2.

Suppose \(f(x) = 3x-2\text{.}\)
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Evaluate each of the following:
  1. \(\displaystyle f^{-1}(1)\)
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  2. \(\displaystyle f^{-1}(3)\)
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  3. \(\displaystyle f^{-1}(0)\)
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  4. \(\displaystyle f^{-1}(5)\)
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  5. \(\displaystyle f^{-1}(4)\)
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Answer.
  1. \(\displaystyle f^{-1}(1)=1\)
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  2. \(\displaystyle f^{-1}(3)=\frac{5}{3}\)
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  3. \(\displaystyle f^{-1}(0)=\frac{2}{3}\)
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  4. \(\displaystyle f^{-1}(5)=\frac{7}{3}\)
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  5. \(\displaystyle f^{-1}(4)=2\)
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3.

Suppose \(f(x)\) is given in the graph below.
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Evaluate each of the following:
  1. \(\displaystyle f^{-1}(0)\)
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  2. \(\displaystyle f^{-1}(1)\)
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  3. \(\displaystyle f^{-1}(9)\)
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  4. \(\displaystyle f^{-1}(2)\)
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  5. \(\displaystyle f^{-1}(4)\)
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Answer.
  1. \(\displaystyle f^{-1}(0)=1\)
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  2. \(\displaystyle f^{-1}(1)=2\)
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  3. \(\displaystyle f^{-1}(9)=5\)
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  4. \(\displaystyle f^{-1}(2)=3\)
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  5. \(\displaystyle f^{-1}(4)=4\)
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4.

Suppose \(g(x)\) is given in the table below.
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Table 4.3.1.
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\(x\) \(-1\) \(3\) \(2\) \(5\) \(4\)
\(g(x)\) \(0\) \(3\) \(7\) \(1\) \(2\)
Evaluate each of the following:
  1. \(\displaystyle g^{-1}(0)\)
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  2. \(\displaystyle g^{-1}(1)\)
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  3. \(\displaystyle g^{-1}(3)\)
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  4. \(\displaystyle g^{-1}(7)\)
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  5. \(\displaystyle g^{-1}(2)\)
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Answer.
  1. \(\displaystyle g^{-1}(0)=-1\)
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  2. \(\displaystyle g^{-1}(1)=5\)
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  3. \(\displaystyle g^{-1}(3)=3\)
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  4. \(\displaystyle g^{-1}(7)=2\)
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  5. \(\displaystyle g^{-1}(2)=4\)
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5.

Suppose \(g(x)\) is given in the table below.
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Table 4.3.2.
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\(x\) \(0\) \(2\) \(3\) \(5\) \(4\)
\(g(x)\) \(0\) \(1\) \(7\) \(5\) \(2\)
Evaluate each of the following:
  1. \(\displaystyle g^{-1}(0)\)
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  2. \(\displaystyle g^{-1}(1)\)
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  3. \(\displaystyle g^{-1}(2)\)
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  4. \(\displaystyle g^{-1}(7)\)
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  5. \(\displaystyle g^{-1}(5)\)
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Answer.
  1. \(\displaystyle g^{-1}(0)=0\)
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  2. \(\displaystyle g^{-1}(1)=2\)
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  3. \(\displaystyle g^{-1}(2)=4\)
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  4. \(\displaystyle g^{-1}(7)=3\)
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  5. \(\displaystyle g^{-1}(5)=5\)
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