3. Iff and g are two lincar functions: f(x)-axtb and g(x)- cx+d, then what are the conditions on a,b.c and d so that f•g=g+f

Q: 6. Let r(x) = 1 + 3r– 10 and s(x) = x- 2. Build a new function, 1(x), for which 1(x)=| State any…

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Q: For what values of a and b will f(x) be continuous on everywhere at x = 2 if the function is x2 – 4…

A: Given f(x) = x2-4x-2x<2ax2-bx+32≤x<32x-a+bx≥3 It is continuous if and only if limx→2-f(x) =…

Q: do you agree with the contention that the functions f(x) = x+2 and g(x)=x2-4 /x-2 are the same in…

A: It is given that, f(x) = (x+2)     and     g(x) = ( x2-4)/(x-2) Then we will prove that f(x) and…

Q: If f is a differentiable function and such that and g(x) = x+2 / 1+f(x) such that f(0) = -2 and…

A: Given: gx=x+21+fx f0=-2 and f'0=5 We have to find the value of g'0.

Q: Suppose that f(x) is a differentiable function such that f'(4)=5 and f(4)=4. If g(x)=xf(x), then…

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Q: 1.4 For which values of a ER is the function f(x+ iy) = (a²x – axy) + i ax? + ay an entire function?

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Q: ,10 If f is a continuous function and F'(x)=f(x) for all x € R, then A 2[F(5) – F(1)] B 2[F(10) –…

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Q: Suppose f and g are functions that are differentiable at x=5 and that f(5)=8 ,f'(5)=-3 ,g(5)=-1 ,…

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Q: If f and g are two functions defined by f(x) = 3x +5 and g(x) = r+ 1, then g(f(x)) is %3D o 9,2 +…

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Q: If we apply Rolle's Theorem to the function f(x) = 2x² – 12x - 7 on the interval [1, 5], how many…

A: 1) From the given problem: fx=2x2-12x-7 ; 1,5   For verifying Rolle's Theorem: If f(x) is a real…

Q: If f'(x) = x(x- 2)(x+1), then the graph of f has points of inflec- tion when x = A. -2 and 1 B. 2…

A: f''(x)= x(x-2)(x+1)2  To find the points of inflection of function f  A. -2 and 1 B. 2 and -1 C. 2…

Q: 2, if x 0 Evaluate the piecewise function at the indicated values from the domain: f(x) = at x=-8…

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Q: Here is a table of values of a differentiable fu F(x) F' (x) 1 3 |7 2 4 7 3 4 Let G(x) = F(F(x)).…

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Q: If f and g are differentiable, then f g is differentiable.

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Q: 4. Given the function f(x) = x3 In x. Determine the following: a. Domain b. X intercept(s)

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Q: and g(x) are differentiable functions, suppose that f(-2) = 1; f(1) = 5; f'(-2) = 3; f'(1) = 3;…

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Q: Suppose f(x) and f'(x) have the following values. -7 -6 -5 -4 -3 4 -9 1 9 2 6 x f(x) -2 f'(x) 1 -2 3…

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Q: Suppose that f and g are functions that are differentiable at x = 12 and that f(12) = 4, f ' (12) =…

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Q: 7. Give an example of two functions h(x) and g(x), such that (h o g) (x) does not exist. E answer.

A: We have to explain by example in this question.

Q: Suppose that g is a function that is differentiable at x = 4 and that g(4) = -2 and g' (4) = 1. Find…

A: We are asked to find the value of h'(4)

Q: For what value of c is the function f(x) = = C= C 7 2-4 (x+2)(x-3) x==2 x = 1 otherwise continuous…

A: Given :fx=c,      x=-27,        x=1x2-4x+2x-3   otherwise

Q: Given that f(x) =x+2 and g(x) = x^2 - x find (f+g) (-3) if it exists

A: The given function:

Q: 34 (a) Show that Deven(x) = t(v(x) + u(– x) is always even. (b) Show that Poda(x) = {(»(x) – v(– x))…

A: The function f is an even function if f(-x)=f(x) and f is an odd function if f(-x)=-f(x).

Q: 8. Show that the function f : N → Q defined by f(n) n- is one to one. n+1

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Q: . Do you agree with the contention that the function f(x)= x +2 and g(x) = x2 -4/x-2  are the same…

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Q: Suppose that f and g are functions that are differentiable at x = 1 and that f(1) = 4, f '(1) = -2,…

A: We have h(x)=f(x) g(x)f(x)-g(x) We take derivative by using the quotient rule and product rule…

Q: If f) (E-1) and g(x) = (-1) then the function () (x) is (2z-5) %3D (2x+5) (2x-5) (2x+5) (x-1) (x-1)…

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Q: 9. Suppose f(x)=x²-14x+49 and g(x)=x-7 . At which of these points does the function y=f(x) g(x) have…

A: The hole in the graph of the function: y=f(x) is the value of x for which the function is not…

Q: 4. Eliminate the arbitrary function f from the following and form the PDE: xy, (a) z = x + y +…

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Q: 11. Decide algebraically if the functions given below are even, odd, or neither. a) f(x) = -7x - 3x3…

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Q: 8. Analyze the differentiability of the following function: f(t) = Vx² – 2 State the restrictions in…

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Q: 7. Give an example of two functions h(x) and g(x), such that (h o g) (x) does not exist.

A: we need to find two functions h(x) and g(x), such that (hog)(x) does not exist. Let us take two…

Q: Please show step-by-step solution

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Q: Based on the graphs of f(x) and g(x), what must the domain of (f. g)(x) be? 10 8 7 6 5 2 g(x) 1…

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Q: If f(x) = |x| + |x – 1| and g(x) is the piecewise function defined by: 2r-1 x> 1 0<x<1 1- 2r x<0…

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Q: Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x2 − 4/x − 2 are the…

A: I am not agreed with this fact that f(x) and  g(x) are the same in every respect. The reason behind…

Q: 2. Suppose that f (3) = 2, g(3) = 5, f'(3) = 6, and g'(3) = -3. Find h'(3) for the following: (a)…

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Q: 4 given that g(2) =1 and g'(2)= - 5, what is F'(2)? If F(x)= g(x)*

A: Just use the quotient rule of derivative and get the required solution. F'(2)=20

Q: Suppose g is an odd function and let h = f ° g . Is h always an odd function? What if f  is odd?…

A: Given  g is an odd function and let h=f∘g. To find  Is h always an odd function? What if f  is odd?…

Q: if r 4,

A: Given,          The function is gx=xif x≤03if 0&lt;x≤13-x2if 1&lt;x≤4x-3if x&gt;4

Q: Theorem 1. If f : R → R is a C² function, then f is conver if and only if f"(x) > 0 for every x E R.

A: As per the company rule, we are supposed to solve only one problem. Therefore kindly repost the…

Q: 4. Suppose that f: X Y is a one-to-one function and that A C X and BC X. Prove that f (AnB) = f (A)…

A:

Q: If we apply Rolle's Theorem to the function f(x) = 2x² – 20x − 2 on the interval [3, 7], how many…

A: We have to apply Rolle's theorem.

Q: If f (x) and g(x) then there exists a constant C such that f(x) = 9(x)+C, for all x. are two…

A: Let us consider h(x) = f(x) - g(x), Then h'(x) = f'(x) - g'(x) Since we have given f'(x) = g'(x),…

Q: If we apply Rolle's Theorem to the function f(x) = 2x² – 20x – 9 on the interval [3, 7], how many…

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Q: Suppose that f and g are functions that are differentiable at x = 1 and that f(1) = 4, f'(1) = -3,…

A: Given h(x)=f(x)g(x)f(x)-g(x)

Q: If the function defined by 6x + 144 x # -24 g(x) = x + 24 k is continuous at x = -24 x = -24, then…

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Q: Suppose that f(x) is a differentiable function such that f'(4)=6 and f(4)=4. If g(x)=xf(x), then…

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Q: Let g(x)= x-2/x+5 and h (x)= x+1/x+5. Then (h+g) (x) is equal to?

A: Topic  =Function

Q: 1. If h(x) = (f(x))² - (g(x))2,f' (x) = -(x) and g' (x) = f(x), then h'(x) = %3D

A: Given h(x) = (f(x))2-(g(x))2 On differentiating both sides , we get h'(x) = 2f(x) f'(x) - 2g(x)…