ab Q4: Show that if f(x) : then fa - fb = f() b-a

Q: find f(x) so that f'(x)=-4e^(x)-6sinx

A: To find f(x) from f'(x) , we have to integrate f'(x) We first separate the integral

Q: The range of f(x)=/4-x² is [0,2] O (-00,2] [2,0) O [-2,0] [-2,2]

A: Range :- set of all output values

Q: 9) Find f(-2). f(x)=3x2 - 8x + 7 My Answer: 10) Given f(x) = x2 - x³, find f(-10). %3D My Answer:…

A:

Q: x2-8 If fx)= X-4 where is f not differentiable?

A: Given the function

Q: 1. How to define the function, f(x, y) = 15x+4x*y+15y 3x+3y to make it a continues function?

A: We have to find the given function is continuous.

Q: Find f. f "(x) = 5/ /1 - x2, = 2 ()- 2. f(x) =

A:

Q: 25. If f(x) = 3x² – x + 2, find f(2), f(-2), f(a), f(-a),

A:

Q: 2-f (x)=x2-2x

A: Given function is f(x)=x2-2x Find the inverse of a given function i.e., f-1(x)

Q: ax+bx+4 ifgと- ニ bx*-2 × ifメ

A:

Q: Find a and b so that the function 1 5x3 — 6х? + 3, х -2 f(x) = ах + b, is both continuous and…

A:

Q: x²+2x=1 then f'(1) is Let f(x) = 2x3+1

A: we have given f(x). And we have to find f'(1)

Q: the function. 4) ((x) = fx+3, for x>0 [x², for x ≤0

A: Given above function is  t(x)=x+3, for x>0x2, x≤0 The objective is to graph the curve.

Q: Example 2:Find f Vx2 – x4 dx

A:

Q: Evaluate the function at the indicated values.

A: The given function is fx=4-3x-6

Q: What is the value of x if f(x) = -3? %3D

A:

Q: tet fz) =-iž, Showthat if z-iz,show thet if f(2) analyticcorno?

A:

Q: 9. If f(x) = e3x, then (f-1)'(x) = %3D 2 А. e3x В. e3x 1 С. 3e3x D. 3x

A: Given: y=e3x for finding given derivative, first we find inverse of given function for that we take…

Q: 3 na of the function f(x) =x3 -x2 - 6x + 12, -3 < x< 3. 2

A: Solution of the problem as follows

Q: A function f is defined by Ax + 5 f(x) 6x - 2 If f(1) = 4, find A.

A: Given: fx=Ax+56x-2  ……1   and, f1=4  ……2   To find: A

Q: Find (a) the domain of  f and (b) f-1 and its domain.   f(x)  = √ (3 -e2x)

A:

Q: éstion 1 If f'(x)=7x x- 4 and f(4)= - 5, then what is f(5) ?

A:

Q: (2x- f(x) = find f'(2)

A:

Q: 1-2x+ x 7-1 3. f(x) =

A:

Q: How will the function f(x)= -(x+4)^3-8 be transformed from its parent function?

A:

Q: Let f(x)=x−3x−−√3f(x)=x−3x3 Can you please show me how to find what values are concave up or down?

A:

Q: 6. If f(x) = x - 1 and gx) 3x + 10, what is f(g(-6))? %3D %3D

A: Given,    f(x) = x2 -1 g(x) = 3x + 10   To find : f(g(-6)) =?

Q: ren f (x) = x2 + 5x + 6, g (x) = x- 3, evaluate (fo g) (2)?

A:

Q: f(x) = -x² + ax + b, x < 2 (-ax + 7, x ≥ 2

A: Here we have to find the value of a and b such that,  f(x)=-x2+ax+b, x&lt;2-ax+7, x≥2 is continuous…

Q: f(x)-f(-1) X-1 Where f (x) = 2x-6

A:

Q: g(x) = 27x2 - x3 concave upward (-x , g) concave downward (g , x)

A:

Q: [4 Let A = * 1. Find f (A), where f(x) = 2x3 + 3x2 + 4x + 5

A: Answer

Q: 172) 1fef(x) = x² + 1. then f'(x) = 3) 2x ble-f 다. 품

A:

Q: What is (go f)(-1) if f(æ) = 2x + 3 and g(æ) = ? %3D

A: When two functions are combined in such a way that the output of one function becomes the input to…

Q: 2 4x f(x) = * - 9 I + 2

A:

Q: If f (x) = v2x, then f"(x) = Jika f(x) = v2x maka f"(x) = ..

A:

Q: Evaluate f √x² - 16 8 -dx

A: use the substitution method for solving the integral.

Q: Find f(x) such that f'(x) = 2x4-7x and f(2)=3

A:

Q: Describe the end behavior for this fucntion F(x)=x^5-3x^3+2x-4

A:

Q: 1. Let f (x) = 2x² – x – 1 and let g(x) = x – 1 Which statement is true?

A: Given, f(x)=2x2-x-1 and g(x)=x-1

Q: 1. If f(x) = 2x – x² and g(x) = |x – 3|, find the value of f(-2) + g(-2)

A:

Q: Al6)- (;) ) A (;) - (:) |zuso -gsino) f) A(3); (xsine +yuno

A:

Q: x-2, xS-2 3) f(x) = %3D (-x-3, x>-2

A:

Q: The range of f(x)= -/2-x² is %3D [-/2,0] O [0,/2] [-2,2] [2, 0) [0,2]

A:

Q: x³+4 Differentiate f(x) using quotient rule. %3D 4х- 5

A: We can differentiate the function using quotient rule as below.

Q: x=-2 of f(x)=√x²-1

A: Above question is solved.

Q: Using the definition f'cx) = lin fCxth ) -fw find f'C4) when fex)=-ax² +3x -7 3. ニーa×

A:

Q: Find f. F"(x) = 20x³ + 12x²+ 4, f0) = 4, ( 1) = -1 Ax) =

A: Let us denote y = f(x). So,…

Q: Find f(x) such that f'(x)=2x4 - 4x and f(2) = 3

A:

Q: 3 Let f(x) = 4.x² 5 and g(x)= 3.x + 7, find. -

A:

Q: С. -5- i.) f (3) = %3D 4-+ ii.) If f(x) = 2 , then x = or %3D 2- -2- %24

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.