5.3E: Exercises
- Page ID
- 104851
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Practice Makes Perfect
In the following exercises, evaluate each function.
- \(f(x)=\sqrt{4 x-4}\), find
- \(f(5)\)
- \(f(0)\)
- \(g(x)=\sqrt{6 x+1}\), find
- \(g(4)\)
- \(g(8)\)
- \(F(x)=\sqrt{3-2 x}\), find
- \(F(1)\)
- \(F(-11)\)
- \(G(x)=\sqrt{5 x-1}\), find
- \(G(5)\)
- \(G(2)\)
- \(g(x)=\sqrt[3]{2 x-4}\), find
- \(g(6)\)
- \(g(-2)\)
- \(h(x)=\sqrt[3]{x^{2}-4}\), find
- \(h(-2)\)
- \(h(6)\)
- For the function \(f(x)=\sqrt[4]{2 x^{3}}\), find
- \(f(0)\)
- \(f(2)\)
- For the function \(g(x)=\sqrt[4]{4-4 x}\), find
- \(g(1)\)
- \(g(-3)\)
- Answer
-
1.
- \(f(5)=4\)
- \(f(5)=2i\)
2.
- \(g(4)=5\)
- \(g(8)=7\)
3.
- \(F(1)=1\)
- \(F(-11)=5\)
4.
- \(G(5)=2 \sqrt{6}\)
- \(G(2)=3\)
5.
- \(g(6)=2\)
- \(g(-2)=-2\)
6.
- \(h(-2)=0\)
- \(h(6)=2 \sqrt[3]{4}\)
7.
- \(f(0)=0\)
- \(f(2)=2\)
8.
- \(g(1)=0\)
- \(g(-3)=2\)
In the following exercises, find the domain of the function and write the domain in interval notation.
- \(f(x)=\sqrt{3 x-1}\)
- \(g(x)=\sqrt{2-3 x}\)
- \(h(x)=\sqrt{x-2}\)
- \(f(x)=\sqrt{-x+3}\)
- \(g(x)=\sqrt[3]{8 x-1}\)
- \(f(x)=\sqrt[3]{4 x^{2}-16}\)
- \(F(x)=\sqrt[4]{8 x+3}\)
- \(G(x)=\sqrt[5]{2 x-1}\)
- Answer
-
- \(\left[\frac{1}{3}, \infty\right)\)
- \(\left(-\infty, \frac{2}{3}\right]\)
- \([2, \infty)\)
- \((-\infty,3]\)
- \((-\infty, \infty)\)
- \((-\infty, \infty)\)
- \(\left[-\frac{3}{8}, \infty\right)\)
- \((-\infty, \infty)\)
In the following exercises,
- find the domain of the function
- graph the function
- use the graph to determine the range
- \(f(x)=\sqrt{x+1}\)
- \(g(x)=\sqrt{x+4}\)
- \(f(x)=\sqrt{x}+2\)
- \(g(x)=2 \sqrt{x}\)
- \(f(x)=\sqrt{3-x}\)
- \(g(x)=-\sqrt{x}\)
- \(f(x)=\sqrt[3]{x+1}\)
- \(g(x)=\sqrt[3]{x+2}\)
- \(f(x)=\sqrt[3]{x}+3\)
- \(g(x)=\sqrt[3]{x}\)
- \(f(x)=2 \sqrt[3]{x}\)
- Answer
-
17.
- domain: \([-1, \infty)\)
Figure 8.7.8- \([0, \infty)\)
18.
- domain: \([-4, \infty)\)
Figure 8.7.9- \([0, \infty)\)
19.
- domain: \([0, \infty)\)
Figure 8.7.10- \([2, \infty)\)
20.
- domain: \([0, \infty)\)
Figure 8.7.11- \([0, \infty)\)
21.
- domain: \((-\infty, 3]\)
Figure 8.7.12- \([0, \infty)\)
22.
- domain: \([0, \infty)\)
Figure 8.7.13- \((-\infty, 0]\)
23.
- domain: \((-\infty, \infty)\)
Figure 8.7.14- \((-\infty, \infty)\)
24.
- domain: \((-\infty, \infty)\)
Figure 8.7.15- \((-\infty, \infty)\)
25.
- domain: \((-\infty, \infty)\)
Figure 8.7.16- \((-\infty, \infty)\)
26.
- domain: \((-\infty, \infty)\)
Figure 8.7.17- \((-\infty, \infty)\)
27.
- domain: \((-\infty, \infty)\)
Figure 8.7.18- \((-\infty, \infty)\)
- Explain how to find the domain of a fourth root function.
- Explain how to find the domain of a fifth root function.
- Explain why \(y=\sqrt[3]{x}\) is a function.
- Explain why the process of finding the domain of a radical function with an even index is different from the process when the index is odd.
- Answer
-
Answers may vary