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: Let f(x) = log₂ (x²+2x+1) and g(z) = log₂(x+1), find h(x) = f(x) + g(x). Oa) h(z) = 0 Ob) h(t) = 2 O…

A: This question can be solved using the concept of logarithmic function.

Q: Use the fact that d lIn x/dx = 1/x, as well as the change-of-base theorem for logarithms, to prove…

A: Given: prove that ddxlogax=1xlna We know that logpq=lnqlnp…

Q: Consider the function f : [0, 2 + e) → [1, 11) given by 2+ 6x – x2 if x E [0, 3) f(x) = 1+ In(x – 2)…

A: We will show the following result

Q: evaluate the Following 'F log p = X and log q=y, x and y. In terms

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Q: The function f:R→R defined as fW)=log_lV\x²+1+x+VVx²+1-x) is

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Q: Calculate f dr for all p > 0 C a (log(

A: In this question, we have to check the given integrals are convergent or not. ∫01/21x(log(1x))pdx ,…

Q: The domain of definition of Rx) = /log (log x)- log (4- log x)- log 3 is %3D (b) [10°, 10*] (d)…

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Q: Let c, fand g be positive numbers such that c + 1. log. fg = log. = log. fº

A: Definition used -               log (m×n) =logm+lognlogmn=logm-lognlog mn=nlogm

Q: If the parent common log function f (z) = log z is shifted 3 units down, what is the range for the…

A: The range of the parent logarithmic function is all real numbers.

Q: (b) Show that u(#) = log log (1 + l#|") belongs to W(U) but does not belong to L(U).

A: Given: u(x)= log log(1 + |x|^-1 )

Q: - 22. Find f'(x) if f(x)= log2 x*- 5 x4- 8 a. f'(x)= (x* – 5)In(2) x*- 5 b. f'(x)= x*-8 12x3 c.…

A: First convert base of log then differentiate

Q: b) Expand log(a+h) by Taylor's Theorem.

A: Consider the expression: loga+h ……1

Q: et f : R → R such that f(x) = 6x° + 5x* + 2(x log x)² + 7. Determine if f(x) is O(x°) and prove your…

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Q: Which of the following are equivalent to log 4+-log x-5 log y? Select all that apply. 3 1 log 4+ log…

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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: Let f(x) = 2log æ+¹ + x + 1, g(x) = 4x²log (32) + 7x log(x²) + 4x, and h(x) Select all that apply.…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: Consider the function g defined by 1 g(x, y) = cos (Tx)+ log3 (x - y) Do as indicated. 1. Determine

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Q: Suppose the functions f, g, h, r and are defined as follows: 1 1(x) = 1093 / +10g, x log3 g(x) =…

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Q: Find the inverse of the following function.f (x) = 3* – 2 Oalf-1 (x) = log, (x + 2) O bl f-(x) = e*…

A: For finding inverse function, solve for x as a function of y. The process is explained in step 2.

Q: Consider the following functions: 1 a(n) = log2(/n) 1 b(n) = (2vm)log2(n) Say which of these…

A: We know the following. Negligible Function: A function f is negligible iff ∀c∈ℕ  ∃n0∈ℕ such that…

Q: - Tuncuon j(x) = xlog x , then f'(1) is a) 1 b) logx c) x d) None of these O d O a O c O b If f(x) =…

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Q: Let f R*R, defined by f(x) = 3*, then f(x) = %3D O log,3 3* o log3x log3

A: See solution below.

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: 2. Expand the following natural logarithms: In(zx'y") b. In- zy а.

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Q: 3. Find the implied domain for the following functions: (a) f(x) = Vx² – x – 6. %3D log, (x – 2) |…

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Q: - Use the fact that d In x/dx = 1/x, as well as the change-of-base theorem for logarithms, to prove…

A: Given : d lnxdx = 1x d logaxdx = 1xlna

Q: (b) Show that u(2) = log log (1 + la|") belongs to W12(U) but does not belong to L (U).

A: Given: u(x)= log log(1+|x|^-1)

Q: UQuestion 2| Differentiate each of the following functions with respect to x a) y = 3x b) f(x) =…

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Q: Verify that for all x, the change-of-base formula holds: loga x for a,b > 0 such that a # 1, b 1.…

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Q: If fx) = r t 1 and g(x) = 8+x logx 1 what is the domain of (fx g)(x)?

A: To find  The domain of (f*g) (x)

Q: 2. Find the domain of the function.(a) f1t2  ln12t  32 (b) g1x2  log1x2  12

A: Given: (a)  f(t)=ln(2t−3)(b)  g(x)=log(x2−1)

Q: At which of the following values of is Log(-1+2) differentiable. Check all the points that apply. z…

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Q: Q1: What is the least integer n such that f(x) is 0(x") for: a) f(x) = 123x² + x³ log x b) f(x) =…

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Q: 2. Show that for any p with 0.5 0 for the function f(a) = plog(1+ æ) + (1 – p) log(1 – a). -

A: We have used Maclarin series in the proof.

Q: I Example 96 The function f:R→R defined as fX)=log.(vvx² +1+x +vVx?+1-x) is (a) one-one and onto…

A: The given function is: fx=logex2+1+x+x2+1-x     ......(1)

Q: Suppose that f (x) is O(g(x)), where f and g are increasing and unbounded functions. Show that log…

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Q: log (xy) = log(x) + log(y) → log(x") = log(x × x x x x . .x x) = log(x) + log(x) + n log(x) ...= N…

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Q: Suppose that log3(x) = 5.3 and log3(y) = 2.1. Evaluate the following exactly, and show your work a.…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Which of the following are equivalent to 5 · log (u-1/6)? Assume u > 0. 1 O log log (u/") 1 log (u")…

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Q: Pls help ASAP

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Q: 8. Prove the following statements. (1) loga = 2 log, r (2) log VI = - log, r (3) log,4 r = log, Vr…

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Q: The domain of function f(x)= log, (x+3) + V5-2x is Select one: O [2.5, 0) O (-3, 2.5] O (-3, x) O…

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Q: Verify the formulas d -[a*] = a* In(a) dx y = a* log,(y) = x. starting with let and the fact log,…

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Q: Which function rule should be used to transform any (x, y) point from f (z) log z to h (z) = -log…

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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: The domain of f(x)= log4(1 – I2) is Select one: O a. ( -1,1) O b[ =1,1] O c. (0, 00) O d. [1, 00)

A: In the question it is asked to calculate the domain of f(x)=log4(1-x2).

Q: (a) By drawing the graphs of the functions f(x) = 1 + In(1 + x) and g(x) = in a suitable viewing…

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Q: Suppose the functions f, g and h are defined by 33 f(x) = 3* + and g(x) = log̟ x + log̟ (x + 6) + 4…

A: In this question, we find the domain of each of the given function f(x), g(x) and h(x). In other…

Q: Find the least integer n such that f(x) is O(x") for the function 3x +x log ax

A: This is a problem of finite math, and complexity.

Q: . Consider the function g defined by 1 g(x, y) = cos (Tx y) + log3 (x - y) Do as indicated. 1.…

A: As per policy, we are allowed to answer only 1 questions at a time. So, I am answering the first…