5. a) Define the following with an example: i) Domain of a function ii) One - to - one function A function fis defined on the det of real numbers by f(x) = 4x+1 2x-3 b) %3D i) Write down the domain of f. ii) Show that f is a one- to - one function. iii) Find the inverse of the function f. c) Given the function f(x) = x2, g(x) = 3x - 4, find the composite %3D function gof(where gofmeans f-1followed by g) d) A function f is defined on the set N of natural numbers by KO) = 2, (2) = 5 and f(n) = 2 f(n - 1) +3 fn - 2) + f(n - 3) for all n 2 3. Find (4).

Q: Find the entire domain on which the function f is one-to-one and non- decreasing. Write the domain…

A: f(x) = (x+3)2 so, f'(x)= 2(x+3)for f'(x)⩾ 0  ⇒ 2(x+3)⩾0                       ⇒ x ⩾ -3Hence,…

Q: Sketch a function that is one-to-one and positive for x Ú 0. Make a rough sketch of its inverse

A: If we take function fx=x2 on the interval [0,∞). This function is one to one and positive on the…

Q: 2. Algebraic Inverses a) Find the inverse f(x) = x² - 4. b) Is the inverse a function? c) Graph the…

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Q: If the function is one-to-one, find its inverse. If not, write "not one-to-one." 12) f(x)= 2 X-5 A)…

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Q: 1. Find the inverse of the following function: f(x) = x² + 2x-4. Restrict the domain of f(x) such…

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Q: HIverse lu ..... 4IDIGGO. O A. O B. C. O D.

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Q: (c) Let U be the set of natural numbers, A be the set positive odd integers and B be the positive…

A: Let's find.

Q: 44) Use the functions defined below to answer the following questions. f(x) g(x) 5 1 8 2 -2 3 8 -7 X…

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Q: Example 2: For f(x)=1/(x-1)²-3: a) Determine the inverse of f(x) and graph each relation. b) State…

A: Given  f(x)=12x-12-3 Here we need to draw a graph and find out the inverse For finding inverse we…

Q: Find the inverse of the function. Is the inverse a function? f(x) = (x + 6)? Choose the correct…

A:

Q: The domain of a one-to-one function g is [0, 15] , and its range is (0, 8). State the domain and the…

A: The domain of a one-to-one function g is 0, 15 and its range is 0, 8.

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.