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: 1 Give one example r that makes log. (r) rational but not an integer

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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 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: 15. If log,8 = 3, what is the value of b? a. 2 b. 4 c. 8 d. 16 16. Given the functions f(x) = (x -…

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Q: Given that a and b are real and unequal and that logab + logba2 = 3, find a relation between a and b…

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

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Q: Write the following as a single logarithm with a coefficient of I. c²b²) 3 log( 2 a²) - 4 log( 2 a…

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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: Suppose f(x) = log(Va- 5) and g(x domain of (f – g)(x). T-25 %3D State the x2-30x ||

A: In the given question, the concept of domain is applied. Domain The set of a function's available…

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: 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: - 2 (410gx = log √ 2² ) + log ³√/x² Write as a single logarithm.

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Q: PleaseDon't use chat gbt

A: Step 1:Step 2:Step 3:Step 4:

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: ems 6. Which of the following is equivalent to 2 log x+logy (1) 2 log xy (2) log 2xy (3) log x²y (4)…

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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: Which of the following functions are Q(x²)?

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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: Express log(x²-x-12) - log(x² - 7x + 12) as a single logarithm. State any restrictions on the…

A: Given : expression  logx2-x-12-logx2-7x-12 Prerequisite : Here we use the formula log a - log b =log…

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…

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A: According to bartleby guidelines we are supposed to do only one question.  If you want more to be…

Q: 2. a) Determine (f= g)(x) in simplified form and state its domain, given f(x) = and g(x) = logx – 2.…

A: Given : (a) f(x) = x/5x+4      , g(x) = log(x) -2 (b) f(x) = 2√(x+9)     , g(x) = (x+2)/(3x+6)

Q: 9. In the graph shown, f(x) = x3 and g(x) = log (x + 3). For what value of x is x³ = log (x+3) when…

A: Consider the function,   Then,          So, by the intermediate value theorem, we can say that there…