The functions f, g, and h are defined as follows. f(x) = |8x - 5|                       g(x) = x^2-2/x+6        h(x) = square root of x-3  +1 Find f−(1/2), g(4), and h(6).Simplify your answers as much as possible.

Q: Find the interval in which the function given by y = 4x3 - 6x2 -72x + 30 is decreasing.

A: Given: y=4x3-6x2-72x+30

Q: Show that the equation f(x) =x+3x-1%=Ø %3D has at least one solution,

A:

Q: The function f(x) = kx* + 8x² has three turning points, a maximum value of 8 and a root at x = 2.…

A:

Q: Approximate the value of the root of f(x)=-3x³+5x²+14x-16 near x=3 to within 0.05 of its actual…

A: Given : f(x)=-3x3+5x2+14x-16, to find the value of the root near x=3.

Q: Find the range of the quadratic function F(x)= 3x^2+6x Use interval notation

A:

Q: The critical point of the function f(x) = a – 6x² + 16x + 13 is %3D - (1, –4) (-2,4) (2, 4) (-2, –4)

A: The critical point of the function y=fx is the point where f'x=0. The power rule of differentiation…

Q: For f(x) = 1- x²

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Q: Consider the function:  f(x)=5x+2   and   g(x)=3x-4  Solve for - (f°g) (x)

A: Given:

Q: 1. f(x) = x3- 3x2 -9x-5

A: NOTE- Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: The graph of f(x) = 2x° + 15x² – 84x + 18 has two horizontal tangents. What is the negative value of…

A: Here, f(x)=2x3+15x2-84x+18

Q: Determine the domain and range of the quadratic function.   f(x)=−4(x+1)^2 − 4   Enter your…

A: We have to find the domain of :  f(x)=−4(x+1)2 − 4.

Q: If f(x)=4x2-2x+3 solve f'(x)=28

A: We first find f'(x) using exponent rule: [d/dx(x^n)= n*x^(n-1)]

Q: The extreme points of the function f(x) = x3 – 6 x² + 9x + 1 are:

A: We have to find the extreme points of the function f(x) = x3 - 6x2 + 9x + 1 .

Q: 1. f(x) = x* – 27x² – 14x + 120 -

A:

Q: Find the equation of the quadratic function f that has its vertex at (3, 5) and contains the point…

A: Given: vertex at 3,5 and it contain the point 2,3

Q: Find the extreme values of f(x) = 5 - 2r2, IS1 lx+ 2, x> 1.

A: Given function is defined in two intervals  So firstly we will discuss  for  x≤1 f(x)=5-2x2 we have…

Q: Find the domain of the square root function and express in INTERVAL NOTATION f(x) = v-3x –- 8

A: The function is given by fx = -3x-8 To evaluate : The domain of the function

Q: Find the range of the quadratic function f(x)= -x^2+4x-6 interval notation

A:

Q: find maximum and minimum of f(x)= 3x2+15x2-36x+10

A:

Q: Solve for the zeroes of f(x) = x* - 4x2 and sketch the graph %3D

A:

Q: Match the quadratic function with its graph. Ax) =-(x-2)2

A: If a parabola has a vertical axis, the standard form of the equation of the parabola is this:…

Q: by graphing the standard quadratic function f(x)=x². Then use transformations of this graph to graph…

A: Please refer to the image below

Q: If one root of f(x) = x2 − 4x + 5 is 2 + i, what else do you know?

A: f(x)=x2-4x+5                                    One root is:=…

Q: Solve f(-2) for f(x) = -5x-4 %3D f(-2) = [?]

A: Given f(x)=-5x-4 To find f(-2) Substitute -2 for x

Q: Find a formula for the quadratic function whose graph has its vertex at (−3,2) and its y-intercept…

A:

Q: What is the maximum value for the function f(x) = -x² + 2x+ 2?

A: The function is given by f(x) = -x2+2x+2 To evaluate : The maximum value of the function.

Q: Find a root of an equation f(x) = 0.582x³ - 0.437x + 2 using

A:

Q: fG)=4x-3 SCx) == (s09) (x)=

A: gx=x2

Q: Find the third degree function that has zeros 7 and -11i, and a value of 663 when x=10

A:

Q: Find sum of two polynomial f(x) = x^3-7x+6 and g(x) = 5x^3-8x+1

A:

Q: Find the absolute Maxima and Minima for f(x) = 2x³ + 21x² + 36x + 10 at [-5, 0].

A: Explanation of the solution is given below....

Q: Solve f(-4) for f(x) = -4x +9 f(-4) = [ ? ]

A: Given: f(x)=-4x+9

Q: 1. Write the quadratic function in standard form.  f(x)=-x^2-4x+1  f(x)=6x^2-x+1

A: Explained below...

Q: What is the equation of a quadratic function y = f(x) with two irrational zeros,-h and h where h is…

A: Given,         The equation of a quadratic function y=fx with two irrational zeros, -h          and…

Q: Suppose​ f(x) is a quadratic function such that its vertex lies on the​ x-axis. How many distinct…

A:

Q: Write the equation for a quadratic function f(x) with roots at r = – 3 and r = – 8 that also passes…

A:

Q: The graph of f(x) = 2x + 6x2 – 90x + 21 has two horizontal tangents. What is the negative value of x…

A: Given that the graph of f(x)=2x3+6x2-90x+21-(i) has two horizontaltangents.Our Aim is to tell the…

Q: 6. If f(x) = 10x – 5, what is f-1(ƒ (3))?

A:

Q: The function f (x) = (x + 6)³ – 2e** has two roots between x = -7 -

A: Solution of the problem as follows

Q: If a ball is tossed in the air modeled by f(x) = -1.5 x2 + 12x + 7 , where height is measured in…

A: The given function is:f(x)=-1.5 x2 + 12x + 7

Q: Solve f(-4) for f(x) = -4x+ 9 f(-4) = [ ? ]

A: f(x)=-4x+9

Q: Solve f(-6) for f(x) = 3x+ 15 %3D f(-6) = [ ? ]

A: Given: f(x)=3x+15

Q: Find the local maximum value of f(x)=x^3-27x+8

A:

Q: Solve for f(-1). f(x) = -3x + 3 %3D

A: The function is given as fx=-3x+3 The objective is to find the value of f(x) at f(-1)

Q: Find the interval in which the function given by h(x)= 4x – 6x – 72x + 30 is decreasing.

A:

Q: fG)=4x-3 , SC)=Ê (3of) (x)=

A: Givenf(x) = 4x - 3g(x) = x2(f∘f)(x) = ?(g∘f)(x) = ?

Q: Sketch the quadratic f(x) = (x-4)² - 5 main points from the parent function, appropriate manner.

A: Topic:- function

Q: Find the point on the graph of the equation f (x) = x² – 8 that is closest to the point (0, -2)

A:

Q: Find a formula for the quadratic function whose graph has vertex (1,−3) and y-intercept −7   f(x)=

A: We have given the vertex (1,−3) and y-intercept −7.

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.