Iff: RR and f(x) = g(x) + h(x), where g(x) is a polynomial and h(x) is a continuous and differentiable bounded function on both sides, then f(x) is one-one, we need to differentiate f(x). If f'(x) changes sign in domain off, then f, if many-one else one-one. 3 If f: R→ Rand ƒ(x) = a₁x + a²x³ +a5x5 +. + a2n + 1x where 0

Q: 2. Sketch a graph of a quartic polynomial function y = fx) such that: € fu) > 0 when - 2 1

A: In the given question we have to draw the graph of a quadretic polynomial s.t f(x)>0 when…

Q: Find the derivative of the function. (x) = (2x – 7)“(x²+ x + 1)5

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Q: If f : R → R is defined by                      f(x) = x2– 3x + 2, find f (f(x)).

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Q: 4. Let f(x)=1+x³-x. Find an x-value that makes f(x) 0.

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Q: Differentiate the following functions. 1. f(x) = x* +5-2 +x -2 +4x4 2. F(t) = (t - 2t + 1)(2t2 + 3t)

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Q: If the product function h(x) = ƒ(x) . g(x) is continuous at x = 0, must ƒ(x) and g(x) be continuous…

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Q: Suppose that f(x) is a function with f(155)=70 and f′(155)=1. Estimate f(157

A: topic -  line and differentiation

Q: If f(x) = x + /2 – x and g(u) = u + v2 – u , is it true that f = g?

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Q: 6. Consider the transformed function g(x)=-3| () +2 of the function f(x)= -(3)', Find the horizontal…

A: We have given function  gx=-315x+2 Horizontal intercept occur when g(x) =0 Put gx=0 -315x+2=0…

Q: = + (-x² + xy 7) =

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Q: Suppose that f(x)f(x) is a function with f(90)=64 and f′(90)=4 Estimate f(92) f(92) =

A: Use the information on f(x) and f'(x) at x=90 to find the approximate value of f(92) (using…

Q: xx+24=5x² fpyonbouy of anyos

A: We have xx+24≤5x2 Consider:…

Q: Prove formally that for all a > 0, function af (x) + g(x) is also a concave function.

A: Let’s say we have a function f(x),  If for every value of x, if f”(x) < 0 then the function f(x)…

Q: Suppose f and g are positive functions. Is the following true or false? Vf,g:N → R f(x) E O(g(x)) =…

A: Big-Θ notation: A function g(n) is in Θ(f(n)) if there exist constants c1, c2, and N such that…

Q: 1 If (x, y)= find f, and f,. Vx? x²+y²

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Q: a. Suppose that ƒ(x) = g(x³) + eg(3x) where g' and g" exist. Find f' and f" in terms of g' and g".…

A: Here we have given a composition of a function as given below.

Q: If f(x) is a linear function, f( – 5) = - 5, and f(5) = – 3, find an equation for f(x) Submit…

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Q: Let f(x) and g(x) be defined as follows: f(x) = 2x+ 1, g(x) = /x-3 What is (fog)(x)?

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Q: V = M2x2 (R) let M = { A€ V A = A²} N = { A = V A = -A ² } Subset of the vector space V V = MON…

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Q: Prove that for all a, b = R, the function f(x) = 3x² - 4x³ + 6x² + ax + b has exactly one point…

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Q: 4. Find the functions f(x), g(x),h(x) that satisfy: f(g(h(x))) = 2.

A: A composite function is created when one function is substituted into another function .

Q: A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f, the tangent…

A: Given problem:- A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f,…

Q: Identify two functions, f and g, h(x) =tan(√x) such that h(x)=f(g(x)): ƒ(x)= g(x)=

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