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Problem 5

Find the domain and range of the function. Then evaluate \(f\) at the given \(x\) -value. \(f(x)=x^{3}-1, x=0\)

Problem 5

Find (a) \((f+g)(x)\), (b) \((f-g)(x)\), (c) \((f g)(x)\), and (d) \((f / g)(x)\). What is the domain of \(f / g\) ? \(f(x)=x+1, \quad g(x)=x-1\)

Problem 5

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. \((-1,2),(5,4)\)

Problem 5

Describe the sequence of transformations from \(f(x)=x^{2}\) to \(g\). Then sketch the graph of \(g\) by hand. Verify with a graphing utility. \(g(x)=(x-2)^{2}+2\)

Problem 5

Decide whether the set of ordered pairs represents a function from \(A\) to \(B\). \(A=\\{0,1,2,3\\}\) and \(B=\\{-2,-1,0,1,2\\}\) Give reasons for your answers. \(\\{(0,1),(1,-2),(2,0),(3,2)\\}\)

Problem 6

Describe the sequence of transformations from \(f(x)=x^{2}\) to \(g\). Then sketch the graph of \(g\) by hand. Verify with a graphing utility. \(g(x)=(x+1)^{2}-3\)

Problem 6

Decide whether the set of ordered pairs represents a function from \(A\) to \(B\). \(A=\\{0,1,2,3\\}\) and \(B=\\{-2,-1,0,1,2\\}\) Give reasons for your answers. \(\\{(0,-1),(2,2),(1,-2),(3,0),(1,1)\\}\)

Problem 6

Find (a) \((f+g)(x)\), (b) \((f-g)(x)\), (c) \((f g)(x)\), and (d) \((f / g)(x)\). What is the domain of \(f / g\) ? \(f(x)=2 x-3, g(x)=1-x\)

Problem 6

(a) plot the points, (b) find the distance between the points, and (c) find the midpoint of the line segment joining the points. \((2,10),(10,2)\)

Problem 6

In Exercises \(5-8\), find the inverse function informally. Verify that \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\). \(f(x)=-\frac{x}{4}\)

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