Let f(x) be a function f:[−1,1]→[0,1], f(x)=x^2. Let g(x):(−∞,∞)→[0,1] be a function such that g(x) is periodic with period of 2 and g(x)=−f(x), for x∈[0,1] g(x)=−f(x), for x∈[−1,0)

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A:

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A: Last option is correct.

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A: Consider the functions, f(t) = et and g(t) = e-8t

Q: 8 Describe the long run behavior of f(x) = x° – 5x* + 5æ° – 1 - - As x → - 0o, f(x) → ? As x → 0,…

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Q: Graph the function h: Z→Z, defined by h(x)=| 3

A: Graph of the function

Q: Determine whether the given set of functions is linearly independent on the interval (-00, 00⁰).…

A:

Q: Let h(x) = f(x)*g(x), and k(x) = f(x)/g(x). g(x) has points (-2,-1), (-1,-2), (1,0), and (3,2). f(x)…

A: see below the answer

Q: For the function f(x) = 6x² + 14x + 31, find f' (x) using the definition f (x + h) – f(x) lim h→0 h…

A: Put values of x as (x+h) in given formula then calculate the expression before put the limit.

Q: Given f(x, y) and y = y(x), we can define a composite functiong(x) = f(x,y(x)).

A: a)Given , gx=fx,yx Then, g'x=∂f∂x+∂f∂yddxyx  [∵y=yx]⇒g'x=∂f∂x+∂f∂yy'x