Given the graphs of f(x) and g (x) below, find the composition of functions f(g(2))

Q: Sketch the graph of the function f(x) = ln 2x  and state its domain.

A:

Q: If f(x)=2-3x². O a. O b. O c. lim h→0 lim h→0 lim 30 From first principles select the correct step.…

A: Given :fx=2-3x2

Q: Draw the graph of f(x) and discuss its differentiability at x = 1

A: It is given that fx=x2x≤1xx>1. Recall the fact that formula for derivative of a function f at a…

Q: Using the criterion of the first and second derivatives, find the graph of the function c) F(x) = x…

A: Topic = Functions

Q: True or false: The graph of the reciprocal function f(x) =1/x has a break and is composed of two…

A:

Q: Sketch the graph of the function y=f(x)=1-x with domain [-1, 1] and range [0, 1]. Find the domain…

A: What is Domain and Range of a Function: For a function depending upon a single independent variable,…

Q: Given the function f, find the slope of the line tangent to the graph of f -1 at the specified point…

A: Given, The function is f(x)=-x2+8 and the point on the graph of f-1(x) is (7,1).

Q: Draw the graph of f(x) and discuss its differentiability at x = 1.

A: Given fx=x2,     x≤1x,   x>1

Q: Consider the functions :  f(x)=√x and g(x)=x-1 Solve for- (f°g) (x)

A: Given:

Q: Find lim h(x), if it exists. f(x) = 4x² + 2x + 6 (a) h(x) lim h(x) = (b) h(x) = lim h(x) = (c) h(x):…

A: We have to find the following conditions according to the given information

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: The graph of f(x) = is (increasing/decreasing) over its domain.

A:

Q: 3. Use the given graphs to sketch the graph of f(x) + g(x). Explain your process. g(x) f(x) + g(x)…

A:

Q: Sketch the graph of the function f(x) = ln x − 3 and state its domain.

A:

Q: Using the attached graph, sketch the derivative. Graph of polynomial f(x) 2 6. -1 -2 -3 -5 -6

A: See the graph whereg graph is increasing f'(x) will be possitive that means it Will be above from x…

Q: Show that the production function f(x) = - () x³ + 10x² + 5x, –∞<x<∞ has both a concave and convex…

A: Given f(x)=-23x3+10x2+5x, -∞≤x≤∞ Consider the function f and its derivative f' can be differentiated…

Q: find the slope of the secant line between x=−1 and x=1 on the graph of the function…

A: Given that the secant line passes between the point x=-1 and x=1 on the function f(x)=-x3-3x2-2x+1.…

Q: Evaluate the limit given

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Q: When the function f(x) satisfies f(1) =1,f'(1)= 3 obtain a value of lim/ (2)" -1 x→1 x² – 1

A:

Q: Suppose that the differentiable function y = g(x) has an inverse and that the graph of g passes…

A: Given,

Q: Explain how to find f (a) geometrically from the graph of y = f (x).

A: Explain how to find f (a) geometrically from the graph of y = f (x).

Q: Given the Graph of the Function: f (x), explain how to obtain the graph of g (a) = -f (x+ 5) +1

A: Given that: Graph of f(x).

Q: (d) lim f(x) x-3 g(x) (e) lim [x²f(x)] x-2 (f) f(-1) + lim g(x) x--1

A: Observe the graph on given limits and see the value of function at the given limits and solve the…

Q: 2. Use the graphs of y=f(x) and y= g(x) to sketch the graph of y=h(x). Hint: Estimate the function…

A: answer is in next step.

Q: Given f(x): 5x² 6x +13, find f'(x) using the limit definition of the derivative. f'(x)=

A: Given problem:- Given f(x)= = 5x²-6x+13, find f'(x) using the limit definition of the derivative.

Q: does y=e9-x2-2 exist? whaet is the domain and range of the function if exists

A: Consider  y=e9−x2−2

Q: Using the graph of f(x) given below lim f(x) = x→2 O 2 O 1.5 1 does not exists

A: Graph of the function is given, we have to find the value of limit at x=2

Q: Find the slope of the graph of the function at the given point.                        f(x) = 27/x3…

A: Given: fx=27x3Point3,1

Q: Find the vertical asymptotes of f(x)= sec(x)

A:

Q: Find lim h(x), if possible. f(x) = -7x2 + 8x – 5 f(x) (a) h(x): %3D lim h(x) = %3D f(x) (b) h(x) =…

A:

Q: 1. Given that f (x) = -x² + 4x, and a = 2, find f(a + h) – f(a) lim h→0 h Explain the meaning of the…

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Q: The graph f(x)- x² is transformed to create m(x) - f(bx)², where "b" is less than 1 but greater than…

A: Given function is                                                                         f(x)=x2…

Q: O f(1) = 3 and lim f(x) = - 2 %3D x-1

A: We have to draw the graph from the given condition

Q: 3. a) Use the Chain Rule and the fact that |x| = Vx2 to show that d dx |x| b) Sketch the graphs of…

A: We will use the give solution as we are instructed.

Q: Find the horizontal and vertical asymptotes.    f(x) x^3 + 1 / x^3-1

A:

Q: Sketch the graph of the function  f(x) = ln∣x∣ and state its domain.

A: Sketch the graph as shown below:

Q: Find the equation of the horizontal asymptote for the function f(x)= 2 - (x / x2 -25)

A:

Q: Sketch the graph of the function f(x) = ln x − 4 and state its domain.

A: Consider the function: fx=lnx-4 To sketch the graph of the function:

Q: 3. If f and are continuous functions with f(3) 4 and lim 2f(x)-9(r)3D5, what is g(3)?

A: To evaluate the value of the function

Q: x+1 If f (x) : Solve to find lim f(x)? Vx2+5-x'

A: We find limit

Q: Sketch the graph of f.

A: A function can be graphed by plotting some points on the function and then joining them with a…

Q: Find the maximum and minimum limits of the function X-2 (x + 2)²

A: Explanation of the answer is as follows

Q: Find the limit of the rational function a. as x→x∞ and b. as x→-. x2 + 11 f(x) = 3 x° + 15 2 + 11 a.…

A: 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: Find the asymptotes of the function f(x)=x/(x−1)2.

A:

Q: Use the graph of the derivative g'(x) shown below and the terminology: increasing, decreasing, local…

A:

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.