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Problem 40

For the following exercises, for each pair of functions, find a. \(f+g\) b. \(f-g\) c. \(f \cdot g\) d. \(f / g .\) Determine the domain of each of these new functions. $$ f(x)=\sqrt{x}, g(x)=x-2 $$

Problem 40

For each pair of functions, find a. \(f+g\) b. \(f-g\) c. \(f \cdot g\) d. \(f / g\). Determine the domain of each of these new functions. \(f(x)=\sqrt{x}, g(x)=x-2\)

Problem 41

For each pair of functions, find a. \(f+g\) b. \(f-g\) c. \(f \cdot g\) d. \(f / g\). Determine the domain of each of these new functions. \(f(x)=6+\frac{1}{x}, g(x)=\frac{1}{x}\)

Problem 41

For the following exercises, for each pair of functions, find a. \(f+g\) b. \(f-g\) c. \(f \cdot g\) d. \(f / g .\) Determine the domain of each of these new functions. $$ f(x)=6+\frac{1}{x}, g(x)=\frac{1}{x} $$

Problem 42

For each pair of functions, find a. \((f \circ g)(x)\) and b. \((g \circ f)(x)\) Simplify the results. Find the domain of each of the results. \(\quad f(x)=3 x, g(x)=x+5\)

Problem 42

For the following exercises, for each pair of functions, find a. \((f \circ g)(x)\) and b. \((g \circ f)(x)\) Simplify the results. Find the domain of each of the results. $$ f(x)=3 x, g(x)=x+5 $$

Problem 43

For each pair of functions, find a. \((f \circ g)(x)\) and b. \((g \circ f)(x)\) Simplify the results. Find the domain of each of the results. \(f(x)=x+4, g(x)=4 x-1\)

Problem 43

For the following exercises, for each pair of functions, find a. \((f \circ g)(x)\) and b. \((g \circ f)(x)\) Simplify the results. Find the domain of each of the results. $$ f(x)=x+4, g(x)=4 x-1 $$

Problem 44

For each pair of functions, find a. \((f \circ g)(x)\) and b. \((g \circ f)(x)\) Simplify the results. Find the domain of each of the results. \(f(x)=2 x+4, g(x)=x^{2}-2\)

Problem 44

For the following exercises, for each pair of functions, find a. \((f \circ g)(x)\) and b. \((g \circ f)(x)\) Simplify the results. Find the domain of each of the results. $$ f(x)=2 x+4, g(x)=x^{2}-2 $$

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