13) Find the inverse functionf- of ƒ. Find the range of f and the domain and range of f-1. f(x) = 3 tan x + 2;

Q: Find f if f"(x) = 2 + cos(x), f(0) = -1, f(π/2) = 2. f(x) =

A: Given differential equation, f''x=2+cosx Boundary conditions are f0=-1, fπ2=2 The formula for…

Q: Graph the function. f(x) = 4 - cos(x)

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Q: $6. Determine the complementary function for the given DE.

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Q: Differentiate the following function 3 - 1 f(x) = sin (x).

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Q: Find f if f"(x) = 2 + cos(x), f(0) = 7, S(x/2) = -6. f(x) = x^2-cos(x)+(-(13-pi^2/4)/(pi/2))+8

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Q: 3. If the function f : R R is defined by the rule f (x) = 4x + 1 for all real numbers x is…

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Q: 1. Determine if the function is even or odd x*+1 g(x) = f(x) = sin x x3-2x

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Q: 2. If f(g(x)) = sin x + 3sinx - 1, determine possible expressions for f(x) and g(x), where g(x) # x.

A: (1st method/way): Let f(x)=x²+3x-1 and g(x)=sinx Then we can find f(g(x)) as follows…

Q: Let f(x) = x cos(3x). Find f' 3

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Q: Sketch a graph of the function f(x) = - 2 sin(a)-1

A: Given: fx=-2sinπ2x-1

Q: Sketch the graph of f. x < 0 sin x, f(x) = {5 - 5 cos x, cos x,

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Q: Write the equation of a function g that is a transformation of f(x) = sin x such that: - the…

A: apply all the shifting and scaling given in the question. Kindly follow the attached image.

Q: 1. Find the intervals on which the following functions have an inverse: (a) f(x) = H2-. (b) f(x) =…

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Q: Show that f is strictly monotonic on the given interval and therefore has an inverse function on…

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Q: 4. Find the intervals on which the following functions have an inverse: (a) f(x) = TFr² " (b) f(x) =…

A: We can use the concept of inverse function in order to solve the given problem.

Q: The range of f(x)= cosx is: *

A: Cosx is a trigonometric function with period 2π.

Q: State the range of the function f(x) = 3 cos ("X 플). O [-1/3,1/3] O (-00,00) O (-3,3] O (-1,1] O…

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Q: Suppose f- is the inverse function of a differentiable function fand let  G(x)  = 1/f-1(x). If f(3)…

A: Let us assume the g is the inverse of function f. Now, f(x)=g-1(x)g{f(x)}=x Differentiate the above…

Q: Q1 Find Maclaurim expression of the function f(x)=tan (x).

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Q: Find the composite functions (fo g) and (g o ). f(x) = x2 – 6 g(x) = cos(x) (fo g)(x) = (g o )(x)…

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Q: Let the function f be defined by tan(x) 1 (x) - sec(x) S"() = -.Write a number.

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Q: Sketch a graph of the function f(x) = 3 cos 6 5 4 3 2 1 -8п -7п -бп -5п -4п -3л -2л -π -1 -2 -3 -4…

A: This question is based on graphing a function from its principal function.

Q: The domain of the function f(x)= tanh( x - 10) is Select one: O[-10, 10] O(0, ) None OR-{10} O [ 10,…

A: Set of values of x for which function is well defined is called domain of the function

Q: Given the functions Ax) = 3* and g(x) - cos X determine the range of the function h(x) - {x) – g(x)

A: The given problem is to find the range of function h(x) = f(x) - g(x) Given f(x) = 3x and g(x)=…

Q: The domain of the function f(x)= tanh( x- 6) is Select one: O[6, *) O[-6.6] O(0, *) OR O None OR-(6)

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Q: Determine the domain and range of function f(x) = elnñ — arcsin (1²²)

A: This question can be solved using the concept of domain and range of inverse trigonometric…

Q: 9) Find f(x) if f'(x) = 7 sin x + 2x - 3 and f(0) = -3

A: Obtain f(x) by integrating the given first derivative as follows.

Q: What is the value of f' () if f(x) tan x 1 1+ 2 Option 1 Option 2 1- 2 2 O Option 3 O Option 4 EIN…

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Q: Compute f' (*) if f(x) =22x sin(x). 2

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Q: Let f(x)={ tan-'(2x) ах+b if x20 if x<0 For which values of а and f(x) differentiable for every real…

A: Option second is correct, a=2 &amp; b can be anything.

Q: Find the domain of the function f(tita) maps to (tan tita) / (2sin tita minus 3cos tita)

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Q: Sketch a graph of the function f(x) = – 1.5 sin(2æ). |

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Q: If you write the function h(x) = tan(2x) in the form h(x) = f(g(x)). then what is the function g(x)?…

A: Given ,  If we write the function h(x) = tan(2x) in the form h(x) = f(g(x))  We have to write the…

Q: Sketch a graph of the function f(x) = sin(x). -7/4 1/4 1/2 3n/4 57/4 37/2 77/4

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Q: The domain of the function f(x)= cosh"'(x/ 3) is Select one: O[3,) O[0,3] O None O[-3,3 ] OR-{3}…

A: The domain of the function f(x): The set of values of x for which the function f(x) is defined.

Q: The domain of the function * sin x f –(x) = g x2 – x + 6 -

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Q: 27) Find the inverse functionf of f with its domain and range. f(x) = cos(x – 3) + 2; 3<x<n+ 3 %D

A: Given that, f(x)=cos(x-3)+2   ,  3≤x≤π+3 Domain of f(x)=[3,3+π] Range of f(x):- Range of f(x)=[1,3]…

Q: Graph the function. f(x) = -3 + cos(x)

A: As we know that if fx transform to fx-a, it means that graph shifts vertically downward by a units.…

Q: 1 g(x) 1 - tan x

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Q: Sketch a graph of the function f(x) 2 cos(Tz) +3 -

A: Given Function :

Q: If f(x) = x tan "x, find f'(3)by first principles.

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Q: if f(x)=cospix, find the extact value of a such that f(1)-f(-1)/1-(-1)=cos a.

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Q: 3. Consider the function for x 0 f(x) = 1 for x = 0.

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Q: Find the intervals on which f is increasing and the intervals on which it is decreasing.​…

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Q: The range of the function f(x)=2- sin 1x is: O a. [-1,3] O b. [-2,2] Oc. [-3,2] O d. [1,3] O e.…

A: We need to find the range of the function f(x).   Range of Sine inverse x is (-pi/2 to pi/2).

Q: Find (f-1)(a). f(x) = 5 + x + tan(rx/2), -1 < x < 1, a = 5 (f-1)'(a) =

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Q: If F(p) = tan-), then find f(x). %3D

A: Start by substituting x for p in F(p)=tan-11p. Assuming, F(x) is the antiderivative of f(x),…

Q: Suppose that f is a function defined as f(x) = xª . drawn to the graph of f at x = 1. Use exact…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: