Let f(x) = vx +1+. Answer the following x-3 questions about f(x): i. Find the domain of f(x) x+0 x > -1, x + 3 O -1 < x < 3 O x#3 O -3 < x < 3 O x> -1, x # 3 (Select the best option) ii. Find and simplify S(x+h)–f(x) Vx+h+l- Vx+h+1+vx+I (x-3)-(x+h-3) Vx +h+1+ x+h-3 Vx+h+1+ x+h-3 I+xA+I+4+x (x-3)-(x+h-3) O OOO

Q: Define f (x) = 4+ x – x² and g(x) = 5x – 3. Define f(x) - - (f o g)(x) = (go f)(x). True False

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Q: 1 |x²-41 1 = a. f(x) b. g(x)= = x²+4x+3 c. h(x) = Vx2 + 5x − 6

A: Answer follows

Q: The function f: RR defined by f(x) = 5x3 + 3x2-x + 7 is O(x). True False

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Q: Consider the functions f(x) = x² 4 and g(x)=√x-2. Which of the following is an element of the domain…

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Q: For which a is each of the following functions defined 2x – 3 (a) f(x) = (b) 1 g(x) = 3x + 2 4.x + 5

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Q: Consider the following piecewise-defined functions: 2x+1, x1 f(x) = g(x): g(0) = Find the following…

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Q: Evaluate the following functions at the given values, and simplify the resultant expressions: a) For…

A: As per company guidelines we are supposed to answer maximum three subparts from a question. for…

Q: Let f(x) = 2x2 - 1 and g(x)= 1 + x². Find (f o f)(x). O x* +2x² +2 4 O 4x4 – 4x2 + 2 | 4 O 2x* + 4x²…

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Q: (a) f(x) =; 2x+1 x²+x-2 (b) g(x) x²+1 (c) h(x) = v4 – x + vx² – 1 %3D

A: The given functions are a.) fx=2x+1x2+x-2 b.) gx=x3x2+1c.) hx=4-x+x2-1 Domain of a function is the…

Q: Sn = .444 ...

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Q: Let f(x) = 2x – 11 + 3(x + 2). Find all values of x for which f(x) is at most 0.

A: Solution: Consider the given function is: f(x) = 2x - 11 + 3(x+2) Simplifying the above we have f(x)…

Q: a. Determine whether f(x) = 5/(x+1) is a one-to-one function from R to R, if not, give a counter…

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Q: Let f(x) = - 4x+ 15 and g(x) =x² +14. Find f(5)- g(5). (5) - g(5) =|

A: Given that: f(x)=-4x+15g(x)=x2+14

Q: Define f (x) = Vx² + 1 and g(x) = 2 – x². Find and simplify (go f)(x).

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Q: 2² – 7x + 12 Explain why f(x) = x – 4 is not the identical function of g(x) :

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Q: 4x + 5 + 5x² – 3 x>5 g(x) =' h(x) =Vĩ - 7x x=5 9x? f(x) = 3x² – 5x +7 4х — 9 x<5

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Q: (4) Let f(x) = xª + 2x³ + 6x² + x – 1. Find, with proof, the number of zeroes of f.

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Q: 1 fiel=r(e² + z² + ; 2-en )dz=? (e is the base of natural logarithm).

A: Let given integral is equal to I

Q: The points of inflection of the function f(x) = 2x - 6x? - 5x 1 is: O 4 O 3 O 2 O 1

A: Find the inflection points of the function

Q: 1 Let f(x) and g(x) = 4x + 5. - 4 | Then (f o g)(6) (f o g)(x) =

A: The solution is given below :

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.