A) Find the Domain of the following functions 1) f(x) = vx – 3+ V5 – x 2) f(x) = 3 – log2 x² – (log2 x)² 3) f(x) = Vx2 –1+ v1- x² - - - |

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: Q2 Determine the equation of inverse function f ƒ (x) = -log; ( - 2x - 3) f(x) = 2 (34x) +6 O Option…

A: given,  f(x)=-log312x-3+4

Q: Let f(x) = log21 (10x + 60) - 15√√x.

A: f(x)=log21⁡(10x+60)−15x

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

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Q: X* Q: Prove that the function y- 2 2 x+1+/log Vx+Jx +1 + log satisfies the relationship 2y=x dx

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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: Evaluate (a) log(2-j3)(6(sin(√ī})² (b) 11/2

A: Given:  log2-j36sinj2 jjj2 To find: We have to evaluate the given expressions.

Q: 14. Let f(x) = log3(9x) and g() = 3". Find f(g(x)) and simplify. %3D (a) 2+x (b) 3+x (c) 9+x (d) 2x…

A: topic- functions

Q: ii) 2 log, (x)– log2 (3x – 4) = log, (x – 1) – 1

A: We make the coefficient 2, exponent inside the log.  And for 1 we replace it by log22 because…

Q: (9) Express the domain of f(x) = log(2x - 4) in interval notation. A (0,2) B (-2,00) C (2,00) D…

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Q: Find the domain of the function of 5 log₂ (4-x²)+11 f(x) = 12x-31-2 + sin¯¹(1 − 2x) Express your…

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Q: For the functions ƒ(x) = log2 (x) and g(x) = log6 (x), where is ƒ > g and g > ƒ?

A: The given functions fx=log2x and gx=log6x We have to find the intervals for which f>g and g>f.

Q: Let ƒ(x) = log₂(x + 1) and g(x) = log₂ (z − 1). Find h(x) = f(x) + g(x). - O a) h(z) = log₂ (21) Ob)…

A: This question is related to Functions, we will solve it using given information.

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: Show that the function is continuous. f(x) = log2(x2 + 1)

A: Consider function  fx=log2x2+1   x fx -4 4.087 -3 3.322 -2 2.322 -1 1 0 0 1 1 2…

Q: dy Q1) Find dx for : 1) y = log3(3x3 + x2)2 x In(sec- x)

A: I supposed to do only first question as our company guideline. Please repost other question as next…

Q: a. Given f(x) = x² − 3 and g(x) = √x + 3. Find (f o g) (x) and write the · domain of (fog) (x) in…

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Q: (1) and (2). Prove, for each pair of expression (f(n), g(n)) below, whether f(n) is 0, 0, or of…

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Q: [5] For each of the following functions f find a simple function g such that f(n) = (g(n)). (a)…

A: Given Data: We need to write Θ(g(n)) for given functions.

Q: A3. (a) (i) Express 2ln x – ln √x as a single log in its simplest form.[

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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: 1 f(t) = log13 (t) and g(t) t - 9

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Q: The function f(x) interval [1, e] at x = Hora lo 0 x is the nat

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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…