Write the domain interval in interval notation. 1. P(x)= log(x2+ 9x + 8) 2. f(x)= log2(x2 - 4)

Q: 3. If ƒ(x) = log₂(−(x − 6)) and g(x) = √(x + ²) a) Determine the domain of g(x) + f(x) b) Is there a…

A: We want to find domain of g+f

Q: 4 Vrite the domain in interval notation of log. ( ), where c > 0. 2-3x,

A:

Q: functions f and g? f(x)=2x

A:

Q: 6. The logarithmic function f(x) = In(x – 1) has the asymptote x %3D

A: Given, Logarithmic function, f(x)=ln(x-1)

Q: 18. Find the domain and range of g(x) log2(x+3).

A: Domain of log is always greater than 0 .

Q: True or False The graph of f1x2 = loga x, where a 7 0and a ≠ 1, has an x-intercept equal to 1 and…

A: Answer: True.

Q: Which of the following represents the domain of h(t)=−log(x)+3?h(t)=-log(x)+3? (0,∞)(0,∞)…

A: We have to find the domain

Q: Find the domain of the function. F(x) = log2 x2

A: To find the domain of the function: F(x)=log2x2 Solution: We know, The logarithmic function is…

Q: b) f(x) = -log2(2x + 3) – 3

A:

Q: Find a so that the graph of f(x) = logax contains the point (2,2) .

A: to find 'a' such that graph of fx=logax contains the point (2,2)

Q: 4. Differentiate the function. f(x) = log3 (x In x)

A:

Q: f(x)=log3(x+6)+log31 and g(x)=2log3(x). For what x-value will both functions have the same value ?…

A:

Q: If f(x) = 1- log5 , then f-¹(x) =

A: Given that a function f(x)= 1 - log5x and we find f-1(x) .   Here i attached the solution of this…

Q: Which of the following is the graph of the piecewise function f (x) - 7 f(x) -2-1 2 1 √-x-1 if XS-1…

A: To plot the piecewise continuous functions: f(x)=-x-1 if x≤-1xx2-x-2 if -1<x<2log2(x-1) if x≥2

Q: (3) Find the domain of f(x) = log(6 + x – x²) (A) (-∞, 3) (B) (-2, 3) (C) (3, ∞) (D) (-∞, -2) U (3,…

A:

Q: Sketch the graphs of ƒ(x) = log2 (x) and g(x) = −log2 (x) in the coordinate plane.

A: Graph of logarithm

Q: Find the domain of f(x) = log(x^2-3)

A: Solve by using properties of logarithmic function

Q: 1. Let f(x) = log2(x). II

A:

Q: The natural logarithmic function f(x) = In x has the asymptote x =

A: Given: f(x)=lnx To Find: Asymptote of f(x). Concept: Vertical Asymptote: x=c is called vertical…

Q: Find the intervals in which f(x) =- is increasing or decreasing. log x

A: the given function is: we have to find the intervals in which the given function is increasing or…

Q: Which of the following is a graph of f(x) = - log3 z - 3? 6. 5- -6-34-3 -2 -1 6. -2- -7 8- 7- -8-7…

A: Put manually  value of x and find f(x)

Q: Find the domain of: f(x)=log7(x-8)

A: Consider the function

Q: f(x) − log2(1 - 3x)

A:

Q: a) Express the new function h(x) = log2(x + 2) in terms of the original function f (X) = log2(x).…

A:

Q: Q1:-genrate and plot the discrete-time exponential Sequance given by x[n]=(0.8)" u(n)

A: To generate and plot the discrete-time exponential sequence given by xn=0.8nun

Q: (2) Evaluate: /- I x" log xdx

A: Authoring guidelines:…

Q: Show that loga (x + √(x2 - 1) + loga (x - √(x2 - 1) = 0.

A: To prove: logax+x2-1+logax-x2-1=0

Q: Sketch the graph of f.

A: Given that, fx=3log3x

Q: Given the functions f(x) = log₂ (2x) and g(x) = 2x - 3, which of the following statements is true?…

A: Here, the given functions are f(x)=log2(2x) =ln (2x)ln 2(used change of base)& g(x)=2x-3 Here,…

Q: 4. Show that the function log(1+ x) lies between functions x - and x for all x > 0. (Hint 2(1+ x)…

A: We will expand log(1+x) by Maclaurin's series. Let f(x) = log(1+x)

Q: Graph the given functions  f(x) =4^x    and   g(x) = log4X  on the same graph b)  Explain the…

A:

Q: 10. Write the domain of the function in interval notation: f(x) = log3 (x2 – 16) %3D

A: We have to find answer

Q: Find the value of x which satisfies the relation  log103+log10(4x+1)=log10(x+1)+1

A:

Q: Find the big O estimate for functions f(x)

A:

Q: Let a ER. Solve the inequality for real values of x. log[x] (x − a) +log[x] (x+a) <0 [...] floor…

A:

Q: Use the graph of f(x)=log1/2x to graph the function f(x)=log1/2(5-x)

A: Since we have to use the graph of f(x)=log1/2x  So, we graph f(x)=log1/2x first. So, we pick values…

Q: 5. Find the domain of f(x) = log(x-4)

A: The given function,   f(x)=logx-4

Q: 8. Determine the domain of f(x) = log;(x² - 2x 15) and write using interval notation.

A: Given, fx =log5x2 -2x-15 We have to find the domain  of f(x)

Q: 5. The natural logarithmic function f(x) In x has the %3D asymptote x %3D

A: Given function - f(x) = ln(x)

Q: What is f(x) of f(x) = log3 (1-2x)²? -32 In(3)-(1-2x)³

A:

Q: 36. Determine the x-intercept(s) of f(x)log2(3x-4)1

A: Rules:x intercept(s): is (are) the point(s) where the graph crosses the x-axis. In order to find the…

Q: Evaluate the function at the indicated value of x= 3. f(x)=log243* -5 5

A: To find the value of given function at x=3.

Q: 5. Prove if the following function is differentiable y = x loge-*

A: Given that: y=xloge-x

Q: Find the domain of f(x). a. f(x) = sqart 42-7x b. f(x) = log3(x - 38)

A: The domain of a function is the set of value of x for which the function is well defined.

Q: True or False The graph of f(x) = loga x, where a &gt; 0and a ≠ 1, has an x-intercept equal to 1 and…

A: Given function is, fx=logax, where a&gt;0 and a≠1.   Use the properties of logarithmic function, The…

Q: 6. Find the domain of f(x) = log, [log, [log3(18r – x² – 77)]]

A:

Q: The natural logarithmic function f1x2  ln x has theasymptote x 

A: Graph of f(x):

Q: Find the domain (in interval notation) of the following functions

A: Domain: Domain of a function is the set of values of x for which the function is defined and real.

Q: 3) For f(x) = log2 x and (x)=√x-4, what is the domain of f(g(x)) and g(f(x))?

A: The function f(x)=logx is defined for x&gt;0 The function f(x)=x is defined for x≥0 Note: If logba=c…

Q: Given that f(x) = log5 x, where x = {-3,-2,-1,0,1,2,3}- a. Find the values of x. b. Sketch the…

A: a) The given expression y=log5x Since the log is always defined for positive values real values of x…