Suppose that the functions fand g are defined as follows. f4) = 3x-4 g(x) =/4x-5 %3D Find f-g and f-g. Then, give their domains using interval notation. (G- 2)(-) = [| Domain of f-g:0 Domain of fg :0

Q: f(x) = 9x² - 4 at x = 1

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Q: Suppose f is a function with property that f(x) ≤ x 2 for all x. Show that  f'(0) = 0.

A: Suppose f is a function with property that f(x) ≤ x2for all x. Showthat f'(0) = 0.

Q: Explain why the function g(x) = ln(4-x2) + square root of x+1 is continuous at every number in its…

A: Consider the given function g(x). The function g(x) is the sum of two functions f(x) and h(x).First…

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A: We need to find where the greatest integer function f(x) = [[ x ]] is not differentiable. We know…

Q: Suppose that f(x) = βx2 − 3     if x ≤ 2                                βx + 2       if x > 2…

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Q: Is it possible to determine f (7) if f (x) = 3 for all x < 7 and f is right-continuous at x = 7?…

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Q: If the function f (x) is continuous for all real numbers and if f (x) x²-4 when x + -2, then x+2 f…

A: f(-2) = -4

Q: is the function continuous at x=5 if f(x)={x2-4x-5/x-5,     x5

A: Given: f(x)=x2-4x-5x-5  ,   x<5x+1            ,  x≥5

Q: Show that f (x) = 2x2 -3 is an even function. Explain why itsgraph is symmetric about the y-axis.

A: Here given fx=2x2-3   A function is said to be an even function if f-x=fx Now…

Q: Find an example of a function on the real line, R, that is contin- uous everywhere except at x = on…

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Q: Find the total number of extreme points for the function f defined as, S-(x* +1)if xs1 f(x) = |(x-3)…

A: Given that, f(x)=-x2+1 if x≤1x-32    if  x>1

Q: Show that f (x) = x3 - 3x is an odd function. Explain why its graph is symmetric about the origin.

A: Given, fx=x3-3x

Q: Determine if f is continuous at x 9 from the right. [5x² f(x) = 3x-27 if x <9 if x29

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Q: If the multiplicity of the function f at the zero p is greater than 1, _f(x) then multiplicity of…

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Q: Find

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Q: . If f : (0, 3) → R is continuous, must its range be an open (possibly infinite) interval?

A: See the detailed solution below.

Q: f(x)%3DX4-3x3 + 2x2 - 5x-7 at x = -1

A: Given:     fx=x4-3x3+2x2-5x-7      at  x=-1 1. f(c) must be defined.  The function must exist at an…

Q: Let f(x) be an EVEN function. If the point (2, 3) belongs to f, then another point likely to belong…

A: Let f(x) be an EVEN function.

Q: Find the constant a such that the function is continuous on the entire real line. 8sin x If x < 0 if…

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Q: The function f  whose graph is given has a discontinuity at x=4 since  does not exist. Prove true…

A: Topic:- function

Q: An even function is symmetric with respect to the________

A: An even function is symmetric with respect to the________

Q: 4. Consider the functions g(x) = and . Determine (12)- (}),

A:

Q: Show that the line y x-1 is an oblique asymptote for the graph of y f(x), summarize all pertinent…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: Given the function,fx=x2+2xx≤14-x1&lt;x&lt;3x-3x≥3

Q: The piecwise function g(x) is defined by x + 2 when x 1. What type of discontinuites are present in…

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Q: Find the intervals on which the graph of f is concave upward. f(x) = In (x² – 2x + 10)

A: f(x)= In(x2 - 2x + 10) To find the intervals on which the graph of f is concave upward.

Q: Check the continuity of the function f(x) at x = -2 f(x) = - 6r + 3x l-6x if xs-2 if x>-2

A: Given,         The function fx at x=-2.           fx=x2+3xif x≤-2x3-6xif x&gt;-2

Q: Suppose that f(x) = βx2-3     if x≤2                                   βx+2       if x &gt; 2…

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Q: If f : [0, 3] → R is continuous, must its range be a closed interval?

A: Given data: The expression for the function is f : [0,3]→R. The continuous image of the open bounded…

Q: Find the roots of f (x) = x4 − 4x2 and sketch its graph. On which intervals is f decreasing?

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Q: Is it possible to determine f(7) if f(x) = 3 for all x &lt; 7 and f is rightcontinuous at x = 7?…

A: Solution: Consider the given that f(x) = 3 for all x &lt; 7 f is right continuous at x = 7  The…

Q: Show whether f(x) is continuous (3х-2 f(x)={ x-2 x² -4 for x=- for x+ -

A: Given that, f(x) = 3x - 2; for x = - 2 f(x) = (x + 2)/(x^2 - 4); for x not equal to - 2 So when x is…

Q: If n= any integer, show that the function f(z) +[- z] has %3D removable discontinuity at x-n, here…

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Q: Suppose that the function fis defined, for all real numbers, as follows. x-4 if x <2 f(x) = - –2x+2…

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Q: Find the function g such that fog = In (2x° +7) if f(x) = In x g(x) = %3D

A: Find the function g such that  f(g(x))= ln(2x3+7) and f(x) = ln(x) .

Q: Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 22x + 4 if x ≥ 2on the closed…

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Q: Find the are under the graph of f(x) = 4-x2  on the interval (-2,1)

A: Given, f(x) =4-x2  we have to find the area under the curve on the interval (-2,1)

Q: Use the function and graph to answer the questions about existence, limits, and continuity. -x-3, -…

A: topic - limits and continuity

Q: Sketch the graph of f'(x) for f(x) = x³ + x³ . Label at least 3 points on this graph .

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Q: Find the limit of the function, f, as x approaches – 3. x2 – x – 12 - - f(x) = x + 3

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Q: Suppose f is a function with domain [a,b]. If f is an odd function, what can be deduced about a and…

A: According to question f is a function with domain [a, b]  And f is an odd function.

Q: Suppose that f(x)=x2 ln(9-5x2) find f'(x) and use interval notation to give the domain of f.

A: Solve the following problem

Q: Suppose f(x) is differentiable everywhere and f(-3) Show f(1) > -6 and f(-5) -2.

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Q: The function has a right-hand limit as x approaches 4. Select one: True False p(x) = x² if 0 < x≤ 1…

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Q: Find the domain of the function using interval notation. f (x) = -2a (x – 3) (x – 5) | | To enter…

A: soution:-f(x)=-2x(x-3)(x-5)To find the domin of f(x)The domain of a function is the set of all…

Q: Suppose that the function fis defined, for all real numbers, as follows. -x+3 if x<-1 -3x+1 if x2-1…

A: Given that: f(x)=-x+3 if x&lt;-1-3x+1 if x≥-1

Q: If f (x) is the function whose graph is shown, on which interval is fincreasing? Use cursor to…

A: f(x) is the function whose graph is shown, on which interval is f increasing?

Q: Determine the open intervals on which the graph of f(x) = (x2 + 1)/( x2 − 4) is concave upward or…

A: To find the open intervals