x +2 if x 20 2x – 1 if x < 0 Determine [g > 2], [g < -2], and [g² < 4]. Q. Given g(x)

Q: B. Find the domain of 1. h(x) = V(x - 2) (x 2 -2 x + 1) 2. (x – 1)(x + 3) 1. 3. If f(x) = -1 and…

A: h(x) = (x-2)x-2 ≥ 0 because square root of -ve number is not defined or a imaginary number.x-2 ≥ 0 x…

Q: 2 2 x >1 4 2x> 2 4 x+ 2 b) f(x) = . 16 52x>4 x² + b 6 2 x > 5 1)is the above function continues at…

A:

Q: III. Given g(x) = 2x² – 3 for x 2 0. 4. Write an equation for g-(x). %3D

A:

Q: (3x - 7x if x< 0 5x - 9 if x2 0 Find g (3) where g (x)

A: Given function is gx=3x2-7x if x&lt;05x-9     if x≥0.

Q: 3. Find [g f](x) for f(a) = 2x +5 g(2) = 2 – 3. and

A:

Q: For what value of x does the function g(x) = (x² – 4)² attain the absolute maximum in the interval…

A: First of all we will see what the extremum value of g will be.

Q: x² -9 f (x) = is 0<x<5 and x=33 at the point 3 x² – 2x – 3° - 1.5

A:

Q: Let h(x)=f(x)+g(x). If f(x)=6x and g(x)=3x2, what is h′(−1)?Do not include "h′(−1)=" in your answer.…

A: we have to find derivarive of h(x) at x=-1

Q: 8. Find the absolute maximum of f(x) = 2x –15x² +24x on the interval [-1, 3]. А. -16 В. 16 С. -41 D.…

A: Differentiate wrt x and put value in the function

Q: Let h(x)=f(x)g(x). If f(x)=−3x2−4x+2 and g(x)=−x2+3x+2, what is h′(−1)? Do not include "h′(−1)=" in…

A: Calculation of h (x):Using the functions f (x) and g (x), the function h (x) can be obtained as…

Q: 4. Given the functions g(x) = 5x +1 find g'(x) 2х -6

A: The given function is: g(x)=5x+12x-6

Q: When g(x) is x+6/2 When f(0) is -3 What is g-1f(0)

A:

Q: from the function f(x) = 3x4 − 4x3 − 12x2 + 5 Find the absolute extreme values of f on the closed…

A: To find out extreme values of f(x) i.e. maximum and minimum values, first we need to calculate…

Q: For g(x) = find g(0), g(1), g(2), g(-1), and g(-2). 4

A:

Q: 3x -2 if - 4sx1 x² + 2x -1 if x< 2 Given f(x) = - and g(x) ={ x+3 5х-3 if x22 x2 find f(0) + g(T).…

A: We can find the answers as below.

Q: G(-2) if g(x) = -x^2 + 4x + 1

A:

Q: g(x) =   5x + 1      find g-1(x)                2x - 6

A: Given gx=5x+12x-6 To find g-1x:

Q: 19. Given g(x) = 3x – 2x, find 9(x+h)-g(x)_ %3D

A:

Q: 5. Given f(x) =-x+ 3 and g(x) = 2x2 – 5, find the value of f (0) + g(1).

A:

Q: B. Find the domain of 1. h(x) = (x – 2) (x 2 -2 x + 1) 2. (x – 1)(x + 3) 1 and g(x) : x + 3 -1 3. If…

A: Domain is the set of all possible values of x (independent variable) for the function.

Q: Given the functions            g(x) =   5x - 2      find g-1(x)…

A: The given function is gx=5x-24x+3. Replace x by y and gx by x and then solve for y as follows.

Q: 4. Find the absolute extreme values of f (x) = x²/3 (4 – x²) on the interval [-2, 2].

A:

Q: x+5 Given f (x) and g(x) = v2x + 3. Find the horizontal asymptote for 2x² +x-45 (x) · g(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: 3. Find the domain of g(x) = v16-x² and h(x) = Vx² – 16. Express your answer using interval…

A:

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

A:

Q: finding the vertical asympnotes for the following; g(x)=x+2/x2 -1

A:

Q: 2-K2 a. h(x) = where k is a constant %3D

A: here we the quotient rule to find the derivative ddxuv= vdudx -udvdxv2  According to our guideline…

Q: 6. Suppose g(x) = 3+ Evaluate g-(-1) 2x – 3

A: This question is related to function and its inverse, We will solve it using given information.

Q: Let h(x)=f(x)g(x) where f(x)=2x2−4x, g(−2)=4, and g′(−2)=−5 what is h′(−2)? Do not include…

A:

Q: x – 1 for x < 1 lV- 1 for x 2 1 - 1 Graph f(x) =

A:

Q: 8. Given f(x) = 3x -9x+35 and g(x)= f(x), determine all possible values for g(5).

A: No real roots

Q: Find g'(4) given that f(4) = -1 , f'(4) = -2 , and g(x) = Vãƒ(x).

A: Use the product rule to find the derivative of the function:

Q: FOR WHAT VALUE OF X does the function g(x) = (x2-4)2 attain the absolute maximum?   X=-1 X=0…

A: We have to find for what value x the function g(x) will obtain a maximum value

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: 11. Find X. (G.8A-S)

A: The triangle proportionality theorem states that the line that is parallel to one side of the…

Q: |x| for x 2 10. g(x) = %3D

A:

Q: If g(x) = √100 - x^2 , where - 10 ≤ x ≤ 0, find A) g^-1 (x) B) the domain and range of g^-1

A: g(x)=100-x2y=100-x2x=100-y2x2=100-y2y2=100-x2y=-100-x2 [here 0≤x≤10]g-1(x)=-100-x2 , 0≤x≤10

Q: - 2x + 4 f(x) find the domain of g(x) – 2x + 2 | - Given f(x) and g(x) -За + 12 - x – 3

A:

Q: if f(x)=2x-6 and g(x)=x-x^2 find the value for g(-1)

A: f(x)=2x-6g(x)=x-x2By replacing he value of x with -1

Q: 6. For g(x) (x+ 7) + óx determine the input for x when the output of g(x) = 13. [ 5A]

A: Given: g(x) = (x+7)2 + 6x   To find : Value of x , when g(x) = 13 That is (x+7)2 + 6x = 13 ⇒x2 + 14x…

Q: l. GRAPH: 1-フ× XCー ー%2 f-1EX=| 5-X if x>l X-3 f6) = 2. GIVEN: f)=3x²2x+5 AND FIND: g6)=4-x a)…

A: Given: (1)  f(x)={x−3    if  x&lt;−1−4x2  if  −1≤x≤15−x   if  x&gt;1(2)  f(x)=3x2−2x+5…

Q: ind the values of k for which f(x) = kx3 -9kx2+9x+3 is increasing on R

A: Definition used -                  Interval of increase -                    A function f(x)…

Q: Suppose f(x) has a zero at an x-value of 3. What would a zero of g(x) be if g(x) = -2f(3x + 1)? %3D

A: Given that f(x) has a zero at x = 3, it means f(3) = 0To find the zero of g(x), where g(x) = -2f(3x…

Q: - g(x) = -2(x+1)+3 arent: ransformations:

A: Given : g(x)=-2 (x+1)2+3 We have to write the parent function and transformations.

Q: G(x)=3/4t+2, find G-1(1)

A:

Q: the intervals where the function is increasing and the interval is decreasing  f(x) = 1/3x^3 - 5x^2…

A:

Q: 1. a) Find the point of inflection(s) of f(x) = x³ – 6x2. If an answer does not exist write DNE) b)…

A:

Q: Let f(x) = 2x + 3. Can you find a number d with the property that , if |x – 1| < 8, then |f (x) – 5|…

A:

Q: Let h(x) = f(x)g(x). If f(x) = 3x² + 2x 3 and g(æ) = ² + 4x + 2, what is h' (-2)? Do not include "h'…

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.