Suppose f and g are differentiable functions on R such that, (x²+1)f (x) + 3xf(x) = e*2 + 7x and (x²+1)g'(x)+ 3xg(x) = e2+ x, on R If f is known, what is g in terms of f?

Q: Let f (*= {(8) +f(9) for real values of x and y. If f '(0) exist 2 2 and equals –1 and f(0) = 1,…

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Q: The functions f₁(x) = x² and f(x)=x³ are orthogonal on the interval [-3,3] ? True False

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Q: Define F : R → R and G : R → Z by the following formulas: F(x) = (x^2)/3 and G(x) = ⌊x⌋ for every x…

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Q: Let f and g be functions defined by, f(x) = Vx+ 2 and g(x) = Vx2 + 1. Find the functions gof, , f +…

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Q: If  f′(x) < 0 for 1 <x< 6, then f is decrescent over(1,6) True or false and why

A: If  f′(x) &lt; 0 for 1 &lt;x&lt; 6, then f is decrescent over (1,6) True or false and why

Q: 3) Let f(x)= 2x+3 . Calculate by definition f'(2).

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Q: Show that f (−1) = f (1), but that there is no point in (−1, 1) where f (0) is zero. Why does this…

A: Given: fx=1-x2/3 So, f-1=1--12/3=1-1=0 Also, f1=1-12/3=0 Thus, f-1=f1

Q: Given f()= 2x + 1 and ()= r*+ 2x-1, fnd (f- (1).Then valute the difence when x=2.

A: Sum and difference of the two functions

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Q: Let f(x) and its linear derivative f'(x) be defined for all real numbers. Use the table of selected…

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Q: Find f" (x) if f (x) = 3(2x¹ + 2x² + 1)¹. 48 (2x³ + x) (2x² + 2x² +1)³ 48 (6x² + 1) (2x² + 2x² + 1)²…

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Q: For any function, With utilization of the product rule for functions of one variable (eq1), show /…

A: Consider the function z=f(x)·g(x) where f and g are both function of x. So we can rewrite the…

Q: Let f (x) = 5x4 + 3x3 + 3x2 + 5x + 5. Fill in the missing coefficients for the derivative of f:

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Q: f(x) |f'(x) | g(x)| g'(x) -4 8 5 -3 10 4 00 3. 3.

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Q: Differentiate f(x) = 4log 3(x)- In (x)

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Q: (g/f)(x) f(g(x)) g(F(x)) f-1(x)

A: As per the bartleby guidelines for more than three parts only three has to be solved. Please upload…

Q: Determine f-¹(x) if 1 (X) = Or¹(x)=x2 X+2 X-3 X-2 or¹(x) X+3 Or¹(x)= X-1 3x + 2 3x + 2 X-1 OM(x)=)…

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Q: (교2 + 3)2r+1 (r – 1)3

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Q: If f(x) = e, how many zeros does f'(x) have on the closed interval [0,2x]? (A) One (В) Two (C) Three…

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Q: 10) Find (¹) (3) if f(x)=x²+x-1.

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