Suppose f : R → R and g: R+ → R are defined by f(x) = x2 + 1 and g(x) = log x – x². What is go f? O a. It is not defined. O b. Defined and gof = log(x²) – (x² + 1)². O c. Defined and go f = log(x² + 1) – (x² + 1)². O d. Defined and go f = (log(x) +x²)² + 1. O e. Defined and gof = log(x² +1) – x?. -

Q: For any real number b > 1, and any real numbers x True False log, (x - y) = > 0 and y> 0, it must be…

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Q: 23. Suppose log5 (A) = x and log5 (B) = y. Express log5 √5A³ B4 in terms of x and y.

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Q: Evaluate the function g√7) given that g(x) = log g(+√7) ? g(47) = (Type an integer or a fraction.)…

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Q: Determine whether each of these functions is 0(x2). Show the witnesses (C and k). a. f(x) = 17x + 11…

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Q: Determine the nature of the following function for even and odd

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Q: Assume you have functions f and g such that f(n) is O(g(n)). For each of the following statements,…

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Q: Condense Conden se into a single logarithm. 4) 6log § x – 31og § y 4.

A: Given 6log8x-3log8y

Q: 7. Find the inverse function for each of the following: (a) y= log, (x+8)-2

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Q: Let h(x) = -2log(3x - 5). Define two functions f(x) and g(x), where h(x) = g(f(x)).

A: Given that,

Q: Find the domain of the function f (x) = log12 (x + 5). O a) D : {x\x -5} OeD: {x\x# -5} O d) D :…

A: Domain Set of all input values where f defined

Q: 22. Find expressions for f(g(x)) and g(f(x)), and state their domains a) f(x)=√√√x;g(x)=x²-4 f(g(x))…

A: Solution :- The domain of a function is the set of input or argument values for which the function…

Q: 8. For each function, determine whether that function is 2(x²) and whether it is (x²). 6.a f(x) = x…

A: Given: Functions ,a) fx=x log x b) fx=x3+x+2To check whether the given functions are Ωx2 and Ox2 or…

Q: Determine whether the statement is true or false. Justify your answer.  a. The graph of the f(x) =…

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Q: Let f(x) = 4log2(x - 3). Shown below are the steps to finding f 1(x). Write the justification for…

A: Describe the each steps as given in steps to find inverse.

Q: Use composition to verity that f (2) = logi(z-5) and g (z) 3 +5 are inverses of each other. Show all…

A: f(x) and g(x) are inverse of each other if (fog)(x) = xand (gof)(x) = x

Q: Which of the following functions are 0(x²)? (Choose all that apply)

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Q: For each of the following pairs of functions, either f(n) is in O(g(n)). f(n) is in (g(n)), or f(n)…

A: Solution:

Q: f(-2) = 3 and g(-2) = –10 f +g)(-2) =

A: Given , f(-2) = 3 g(-2) = -10

Q: Suppose the functions f, g, h and I are defined as follows: f(x) = 4x²-5x+1 g(x) = h(x) = +3 1(x) =…

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Q: g(x) = 2 (log x)< + 5x< log x+ 8x a. Show that g(x) is not O(x²). b. Show that g(x) is O(x³). c.…

A: we have given g(x)=2(logx)2+5x2logx+8xa. logx grows at lesser rate than x we consider Highest degree…

Q: Express the function h(x) = 5log(x² + 6) the form fog. If f(x) = 5log(x), find the function g(x)

A: We can find the function g(x) from the given composite function in the below steps.

Q: Determine the nature of the following function for even and odd f(x)=log(x+vx°

A: if f(-x) = f(x) then f is even  if f(-x) = -f(x) then f is odd if if f(-x) is not equal to f(x) and…

Q: Let x = log 3 and y = log 4. Express the following in terms of x and y.     Please provide all…

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Q: 2) Describe in words the following transformations to f(x) = log.x: a) y = 2log[-2(x − 1)]. b)…

A: 2 (a). Given,                      y=2log-2(x-1).

Q: If f(x)=10*+²-5 and g(x)= log(x+5)-2, show that the functions are inverses of one another using…

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Q: 4. We have seen in lectures that the differentiation of a function given by valid power series…

A: If limn→∞ |an+1an|=Lwhere L is a positive real number or L=0 or L=∞, then the power series…