QuestionJune 7, 2025

For the given functions f and g, complete parts (a)-(h) For parts (a)-(d) also find the domain f(x)=(5x+8)/(8x-5);g(x)=(8x)/(8x-5) (f) Find (f-g)(2) (f-g)(2)=(2)/(11) (Type an integer or a simplified fraction.) (g) Find (fcdot g)(1) (fcdot g)(1)=(104)/(9) (Type an integer or a simplified fraction.) (h) Find ((f)/(g))(4) ((f)/(g))(4)=square (Type an integer or a simplified fraction.)

For the given functions f and g, complete parts (a)-(h) For parts (a)-(d) also find the domain f(x)=(5x+8)/(8x-5);g(x)=(8x)/(8x-5) (f) Find (f-g)(2) (f-g)(2)=(2)/(11) (Type an integer or a simplified fraction.) (g) Find (fcdot g)(1) (fcdot g)(1)=(104)/(9) (Type an integer or a simplified fraction.) (h) Find ((f)/(g))(4) ((f)/(g))(4)=square (Type an integer or a simplified fraction.)
For the given functions f and g, complete parts (a)-(h) For parts (a)-(d) also find the domain
f(x)=(5x+8)/(8x-5);g(x)=(8x)/(8x-5)
(f) Find (f-g)(2)
(f-g)(2)=(2)/(11) (Type an integer or a simplified fraction.)
(g) Find (fcdot g)(1)
(fcdot g)(1)=(104)/(9) (Type an integer or a simplified fraction.)
(h) Find ((f)/(g))(4)
((f)/(g))(4)=square  (Type an integer or a simplified fraction.)

Solution
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Answer

\frac{7}{8} Explanation 1. Define (\frac{f}{g})(x) (\frac{f}{g})(x) = \frac{f(x)}{g(x)} = \frac{\frac{5x+8}{8x-5}}{\frac{8x}{8x-5}} 2. Simplify the expression Cancel out the common denominator (8x-5): \frac{5x+8}{8x} 3. Evaluate at x=4 Substitute x=4: \frac{5(4)+8}{8(4)} = \frac{20+8}{32} = \frac{28}{32} = \frac{7}{8}

Explanation

1. Define $(\frac{f}{g})(x)$<br /> $(\frac{f}{g})(x) = \frac{f(x)}{g(x)} = \frac{\frac{5x+8}{8x-5}}{\frac{8x}{8x-5}}$<br /><br />2. Simplify the expression<br /> Cancel out the common denominator $(8x-5)$: $\frac{5x+8}{8x}$<br /><br />3. Evaluate at $x=4$<br /> Substitute $x=4$: $\frac{5(4)+8}{8(4)} = \frac{20+8}{32} = \frac{28}{32} = \frac{7}{8}$
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