Find f+ g, f– g, fg, and f/g and their domains. f(x) = x, g(x) = Vx Find (f + g)(x). Find the domain of (f + g)(x). (Enter your answer using interval notation.) Find (f – g)(x).

Q: 1. Let glø) = x² - 5x +2.

A: Given that: g(x)=x2-5x+2

Q: Find the open intervals on which the function is increasing or decreasing            f(x) = x2 + 3x…

A: We find f'(x) using the power rule

Q: Use the graph of f(x) = 2x to obtain the graph of g(x) = 2x + 1.

A: g(x)= 2x + 1 = f(x)+1 This means f(x) will move 1 unit up to make g(x). Graph of f(x) is:

Q: Use the graph of f(x) = lxl to obtain the graph of g(x) = lxl + 3.

A: g(x)=|x|+3= f(x)+3 So, this means f(x) shifted 3 units up to make g(x).

Q: Find the constant a such that the function is continuous on the entire real line. - [8x², a = ax -…

A:

Q: Find the open intervals on which the function is increasing or decreasing.     g(x) = x2 − 2x − 8

A:

Q: If f(x) = x3 - 2x - 5, find f(2) and f(3). Then explain why the continuous graph of f must cross the…

A: Given  The function is f(x) = x3 - 2x - 5 .

Q: 2+ and g(x) = Figure out the domain of (fog)(x) in which f(x) = 4-x2

A: Given f(x)=2+x4-x2g(x)=1xHere…

Q: Find the maximum or minimum value of the function. f(x) = 3 - 4x - x2

A: f(x) = 3 - 4x - x2

Q: Let: f(x)=x² +, f'(x) =2x-- 21 f"x)=2+ 1. Find x- and y- intercepts of the graph of f, if it has…

A:

Q: Find the domain of the function. 4 + X g(x) = 1 - X

A: The given function is The domain of the function is set of input values for which the function is…

Q: Find the absolute maximum and absolute minimum values of the function f(x)=2x-13ln(8x)  on the…

A:

Q: Find the absolute maximum and minimum values of the function, if they exist, over the indicated…

A:

Q: Find the open intervals on which the function is increasing or decreasing.

A: A function f(x) is:  (i) increasing on an interval (a, b) if f'(x)>0 for all elements of a, b.…

Q: Find the intervals on which the function f(x) = x² - 6x + 10 is increasing and decreasing.

A:

Q: 4 Find the domain of f(x) x + 3

A: Given:  fx=4x+3 To Find: Domain of the given function fx

Q: Find the inflection point, if it exists, of the function. (If an answer does not exist, enter DNE.)…

A:

Q: 20.) Find function the Ceroes algebraically. of the f(x) = x² - 6x +8 4x X = ?

A:

Q: x - 7 If f(x) = Vx – 3 and g(x) find the domain x - 4 of

A: Given: f(x)=x-3 and g(x)=x-7x-4 To find: Domain of fgx.

Q: Use the graph of f(x) = 3x to obtain the graph of g(x) = 3x-1.

A: The given function is fx=3x. The graph of the function as shown below:

Q: Find the intervals on which the function f(x)=x3+1x3 is strictly decreasing.

A:

Q: 2. Find the Domain of the function: h (x) = 4x x (x² – 9)

A: Given function h(x)=4xx(x2-9)

Q: Use the graph of f(x) = 3x to obtain the graph of g(x) = 3x-1

A: Given: fx=3x, gx=3x-1 for drawing graph of given gx, first we simplify gx so, gx=3x-1=3x.3-1=3x3

Q: 7. Find the domain of f(x) = V² + 2x – 3 and write it in interval notation.

A: The solution is given below.

Q: Q2/A/ Find the intervals on which the function f(x) = x² - 4x + 3 are increasing and the intervals…

A:

Q: (-2x² – 5x + 14,x 3 x= 3 continuous at x = 3. Justify the conclusion.

A: For given function f(x) ; -2x2 -  5x  + 14  , x < 3   .... (i) 19  , x = 3         ..... (ii)…

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A:

Q: Use the graph of f(x) = lxl to obtain the graph of g(x) = 2lxl.

A: Solution: Consider the graph of function f(x) = x which shows in the pink color below. Now, define…

Q: Find the intervals of increase and decrease for the given function. f (x) = x2 + 4x + 3

A: A function is  increasing on an interval, where the value of the first derivative of the function…

Q: Find the asymptotes of the function f(x)=3x2−2x+1x−1

A:

Q: find c such that f(x)=-0.2x2-3x+c has a maximum value of -224. what is the value of c

A:

Q: 2. Let -x2 12x – 32, x 6 2 (a) Sketch the graph of f. (b) Identify the domain, range, and zeros of…

A:

Q: Find the local maximum and minimum values of the function f(x)=-3x2+4x+5.

A: If second derivative negative then local maximum value

Q: Find the open interval(s) on which f(x) = - 5x+ 50x +8 is increasing or decreasing.

A: Given that:

Q: 3. Given f (x) = 5x² and g(x) = Vx – 3 , what is the domain of (f • g)(x)? Write your answer in…

A: f(x)=5x2, g(x)=x-3

Q: On what interval is f(x) = x³ + 3x² – 24x +7 decreasing? The graph is decreasing on the interval

A: Use first order derivative test to obtain the interval of decrease.…

Q: Use the graph of f(x) = lxl to obtain the graph of g(x) = -lxl.

A: The given function is fx=x.

Q: If fx) is a differentiable function such that f(-2)=-1 and g(x)-f(3x+1), then what is g'(-1)?

A: Use chin rule to differentiate g(x).

Q: Find the intervals of monotonicity of the function f(x)=x3−12x+5.

A:

Q: Suppose k>0. What is the domain of F(x) =/k² – x² ?

A:

Q: Find the absolute extrema of the function g(x) = -10x/x^2+9 on the interval (-5,2)

A:

Q: Find and classify the extreme values of f(x) = 6x4 – 4x over the interval [-2, 2].

A:

Q: The function f(x)=-4x3-30x2+72x-6  is increasing on the interval ( ?, ?) It is decreasing on the…

A:

Q: Find the intervals of concavity of the function g(x)=2x4+9x3

A:

Q: Find the open intervals on which the function is increasing or decreasing.       y = x√(16 − x2)

A: The given function is , y=x16-x2

Q: Identify the open intervals on which the function is increasing or decreasing. g(x) = x² - 8x - 20

A:

Q: Find the asymptotes of the function f(x)=x3 / x2+1.

A: Since the degree of numerator (3) is greater than the degree of denominator (2), therefore there is…

Q: Let f(x) = 2x³ - 3x² - 120x+7. a. Find all points on the graph of f(x) at which the tangent line is…

A:

Q: Find the open intervals on which the function is increasing or decreasing.        h(x) = 12x − x3

A: Given function - h(x) = 12x-x3let's find the critical point of the function h(x) , by h'(x) =…

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.