1. Given that f(x)=Vx-3 and g(x)= 4+3x , perform each of the following operations and give the domain (in interval notation) of the combined function: a. (f g)(x) b. (f+g)(x)

Q: Evaluate the piecewise function at the given valu 2x+ 4 if x<0 f(x) = %3D 2x+5 if x2 0 (a) f(-4) (b)…

A: Given f(x)=2x+4 for x&lt;0 and 2x+5 if x≥0f(-4), here -4 is &lt;0. So, we have to substitute -4 in…

Q: A liquid form of penincillin manufactiured by a pharmaceutical firm is sold in bulk at a price of…

A:

Q: If f'(x) = 2x- x-2, then f has inflection point(s) with x – coordinate(s) equal to

A:

Q: Consider the functions :  f(x)=√x and g(x)=x-1 Solve for- (f°g) (x)

A: Given:

Q: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

A: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

Q: Determine all the critical points for the function. f(x)=6x^5+33x^4−30x^3+100

A: We have to determine all the critical points for the function  f(x) = 6x5 + 33x4 - 30x3 + 100 We…

Q: (4) For the functions f(x) = Vx- 3 and g(x) = Vx+2, find and determine the domain %3D in each case:…

A: As you have asked multiple question, we will answer first question only. lf you want any other…

Q: Determine h(1) and h'(1). h(x) = [f (x)]2

A: The function h(x) is a composite function since its input is another function f(x). Now h(x)=[f(x)]2…

Q: 2) Find the domain only for the following functions: x + 3 V2x + 5 Vx -2 1) у3D 2) у %3 3) у %3 x -…

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

Q: Locate the discontinuities of the function. 2 f(x) = 1 + e7/x

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Q: Зах + 3 for x -2

A:

Q: Find the domain of the function. 29) f (x) = v25 – x2 30) f (x) = 3x + 4 31) h(x) 32) h(t) = |t + 1|…

A:

Q: 2 2 V1-x 1-х

A: ∫un du = un+1n+1+C ∫cos(au) du =1asin(au)+C

Q: Find the value of the constant (a , b, or c) that makes the function continuous.

A: the given function is: fx=x2-c          for x&lt;54x+2c      for x≥5 we have to find the value of c…

Q: b- Determine the critical point of the function f(x) = x5 – 5x* + 5x³ –- 1 %3D

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Q: 2. If f (2) = 10 and f' (x) = x²f (x) for all x, find f"(2).

A:

Q: Find the maximum and minimum values of the function f(x) = x² – 6.x +7 on the interval [0, 5].

A: It is given that, f(x)=x2-6x+7   , on the interval 0,5We have to find the maximum and minimum values…

Q: 2) Find the domain only for the following functions: x+3 V2x + 5 Vx -2 1) у%3 2) у %3 3) y = x - 2x…

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Q: Consider the function y = (x) where f(x) = x³ +2x2 - 4x and g(x) = x2 + 2. Determine a) the domain…

A: The domain of definition of a function is a set of those values for which we can define a function.…

Q: 2. Use the graph of the function f(x) to estimate where (a) f'(x)= 0, y f(x) (b) f'(x) 0.

A: (a) f'(x) =0   =&gt; the slope is zero, it means when the graph is parallel to x-axis  i.e. at…

Q: Suppose the total cost C(x) (in dollars) to manufacture a quantity x of weed killer (in hundreds of…

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Q: For function f (x, y) = y2 x2 +1

A: Please refer the attached image for complete solution.

Q: Find the values of x for which the function f (x) = x −7/x^2 + 3x −70 is continuous.

A: Topic:- function

Q: Given the function f(x) = 3 %3D when it could be discrete

A: Given f(x)= 3x+7 Now we write a real world problem for the given function In the given function , 7…

Q: 3. Find the exact area of the piece of land in San Francisco, Surigao del Norte which is bounded by…

A: Topic:- application of integration

Q: Find f'(a) for x2 f(x) = x + 6 at a = 3.

A: Given function :

Q: Find the value for k so that the function will be continuous at x = 2. 4x + 16 if x 2

A: The function fx is continuous at x=a, if limx→a-fx=limx→a+fx It is given that fx=4x+16if…

Q: What happens to the function f (x) = 1 + as x approaches to zero.

A: The definition of the function gx=x is given by, gx=x for x≥0=-x for x&lt;0 Thus, the left hand…

Q: Determine if the given function is differentiable at a = 1 4 – 2x, if x 1

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Q: 19) If f(x) = 3x + 1 and g(x) = 5 – x°, find g(f(x)).

A: Given:

Q: DERIVE THE F. FUNCTIONS: s) y (x-3)(3x+4)(x²-2x+ 1)

A:

Q: if the function f(x)= x^3+ax^2+bx has the local minimum value -2/9 cube root 9 at x= 1/cube root ,…

A: Given fx=x3+ax2+bx has local minimum value -239 at x=13 to find  value of a and b explanation as…

Q: X+1 5) Is the function given by f(x) x2 - 8x + 15 continuous at x = 3? Why or why not?

A: f(x)=x+1x2-8x+15

Q: 2 If f'(x) = 3x? and X f (1) = 0, find f (x

A: Given  f'(x) = 3x2 - 2x3 ... (1) f(1) = 0

Q: The interval in which the function is decreasing is at x2 бх + 1 2 x3 y = 3

A:

Q: Derivatives

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Q: Given the function: 0 < x < f(x) = 5<x< n 2 п — х

A: Given that f(x)=x,    0&lt;x&lt;π/2π-x,  π/2 &lt;x&lt;πTo the plot the graph and find the fourier…

Q: Find the absolute maximum of the function f(x) = xª – 8x² on the interval –1 < x< 3.

A:

Q: For what value of the constant c is the function f continuous on (-0, ∞)? ( cx2 + 8x if x < 5 f(x)…

A: Given f(x) = cx2+8x   if x&lt;5x3-cx  if x≥5               we find the constant C is the function f…

Q: 2. Given the function y = x²[2f (x) + 3x]*. If f (1) = -1 and 54 for x = 1, %3D determine f'(1).

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Q: f(x) = x* – }x' – x + 2x –1 -

A: Given   f(x)= 14x4-23x3-12x2+2x-1has turning point at where the f'(x)=0differntiate f(x) with…

Q: Find a number c that satisfies the conclusion for f(x) = x + x-1 on the interval [0, 2]

A: Answer is 2/√3

Q: Given that f(x) = 2x-2n + 8x², what value should be assigned to n to make f a function of degree 3?

A: Given f(x)=2x-2n+8x2. We need to find what value of n makes f(x) a function of degree 3.

Q: Find the global extrema of the function f(x)=3x4−6x2+2 on the interval [−2,2]

A: Global extrema of a function exists at critical points or at the end points of the interval.…

Q: Find the x-values of the stationary points of the function  f(x) = x^4 + 4x^3 - 4x^2 - 24x

A: Given: f(x)=x4+4x3−4x2−24x

Q: For what value of x does  function g(x)= (-1/3)x^2+2x^2 convex?

A: please see the next step for solution

Q: What is the domain of the function f(x) = %3D 5" Vn n-1

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Q: n x(0)=0

A:

Q: Determine h(x – 1) for the following function. - - 2x h(x) = %3D x2 - 7x + 12

A: the given function is: we have to determine h(x-1) for the given function.