For f(x) = 1/(x^2−4) and g(x) = √ (x − 1), determine the subset of the domain of g on which the composition f ◦ g is well-defined, and then determine the subset of the domain of f on which the composition g ◦ f is well-defined. In other words, determine the domains of f ◦ g and g ◦ f. Then, find formulas for (f ◦ g)(x) and (g ◦ f)(x).  • If you use a definition, explicitly cite it by using the phrase “by the definition of . . . .” • If you use a theorem (or a rule, a test), explicitly cite it by using the phrases “by theorem . . . .” • Explain the quantity each symbol represent in word problems. Use phrases like “let x be the height of a rectangle” or “let t represent time in seconds.”

Q: If g(a)= b and f(b) = c, then explain how to find (f og) (a)

A: Given g(a)= b ......(1) f(b) = c .....(2)

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A: Given:

Q: write down the power seires for (x)(f(x))

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Q: Let f(x) = (x + 5)?. Find a domain on which f is one-to-one and non-decreasing. Find the inverse of…

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Q: 3. Consider the relation f (x) = 2x² – 4. Find the f(x). Be sure to use proper notation.

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Q: 1. for f(x)=x2 + 2 AND g (x)= 8 - 7x, evaluate:  a) g(-3a + 1) b) g(-3a + 1) - f(a+4) c) x when…

A: “Since you have asked multiple questions, we will solve the first question for you. If youwant any…

Q: 2 Let f(x)=Vx and g(x)=- x-4

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Q: consider the functions f (x) =5/x and g(x)= x/x+2 A) evaluate and smiplify (f+g)(x) and state the…

A: fx=5x,  gx=xx+2 f+gx=fx+gx f+gx=5x+xx+2 f+gx=5x+2xx+2+x2xx+2 f+gx=5x+2+x2xx+2 f+gx=5x+10+x2xx+2…

Q: Consider the function f(x)=√x+5-9 for the domain [-5, ∞0). Find f¹(x), where f -1 is the inverse of…

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Q: Let f(x)=2x^4-4x^3-5x^2+2x-3. Define g(x) to be the restriction of f(x) to the largest possible…

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