1) Graph \(f(x)=2(x-3)(x+1)\) and its inverse on the same coordinate grid. Then use the graphs to answer the following questions:
a) Describe how you determined the inverse graph.
b) Is the inverse of f(x) a function? Explain.
2) Graph \(g(x)=x^3-1\) and its inverse on the same coordinate grid. Then determine if the inverse of \(g(x)\) is a function.
3) Determine whether the inverse of each graph is also a function.
a) b) c)
a) Describe how you determined the inverse graph.
b) Is the inverse of f(x) a function? Explain.
2) Graph \(g(x)=x^3-1\) and its inverse on the same coordinate grid. Then determine if the inverse of \(g(x)\) is a function.
3) Determine whether the inverse of each graph is also a function.
a) b) c)
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Write the inverse of the following functions:
4) \(f(x)=3x-6\)
5) \(g(x)=-2x+7\)
6) \(h(x)=\frac{4}{3}x-2\)
7) \(j(x)=x^3-4\)
8) \(k(x)=(x-3)^3+1\)
9) \(l(x)=\sqrt[3]{\frac{x}{4}}+5\)
10) Given \(f(x)=x^3-8\) and \(g(x)=\sqrt[3]{x+8}\), use composition of functions to determine if \(f(x)\) and \(g(x)\) are inverses.
11) Given \(f(x)=-x^5+3\) and \(g(x)=\sqrt[5]{x-3}\), use composition of functions to determine if \(f(x)\) and \(g(x)\) are inverses.
12) Find the inverse of \(m(x)=4x^5-1\).
13) Graph \(f(x)=x^2+2\) with a restricted domain so that \(f^{-1}(x)\) would be a function. Be sure to state what your domain restrictions are.
14) Given \(f(x)=x^2-6\)
a) Write the inverse of \(f(x)\).
b) Explain why the inverse of \(f(x)\) is not a function.
c) Write \(f^{-1}(x)\) when \(x\ge0\).
d) Write \(f^{-1}(x)\) when \(x\le0\).
e) How does restricting the domain of \(f(x)\) allow \(f^{-1}(x)\) to be a function?
15) Given \(g(x)=\frac{1}{2}x^2+9\); \(x\le0\), find \(g^{-1}(x)\).
16) Given \(h(x)=3x^4-8\); \(x\ge0\), find \(h^{-1}(x)\).
Review
Simplify the following expressions:
17) \(\large{\frac{4x^{\frac{1}{2}}y^{-\frac{5}{3}}}{14x^{-\frac{3}{2}}y^{\frac{7}{6}}}}\)
18) \(\left(\frac{27}{64}\right)^{-\frac{4}{3}}\)
19) Convert \(y=3(x-5)^2-21\) to standard form.
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