Prove the Root Theorem: For any f(x) ∊ F[x] and any a∊F, f(a)=0 if and only if x-a is a factor of f(x).

Q: f is a function of all real numbers defined by f(x)=x2, what is f-1({x |0<x<1})?

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Q: 4. Lėt f:A total injective function. B and g: B→C be two functions. If gof is a bijective function,…

A: we know that  gof is Bijective,  hence, gof has one to one correspondence,  This deduces that g must…

Q: Find (a) the domain of  f and (b) f-1 and its domain.   f(x)  = In  (2 + In x)

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Q: Viewed as a function f: R → R, a polynomial of odd degree is always surjective. True False

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Q: Viewed as a function f: R → R, a polynomial of even degree is never injective. True False

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Q: We know that 1 is a zero of the function f(x) = x3 + x2 - 5x+3 the multiplicity of f at 1 is: Select…

A: We are given that 1 is a zero of f(x)=x3+x2-5x+3 ⇒(x-1) is a factor of f(x)=x3+x2-5x+3 Now, By long…

Q: Determine the value(s) of x such that  [ x  2  1 ] [ 2   0  -2] [ x ]                 [ 0   3  3 ]…

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Q: Let f be a function defined on the real line R and suppose that it satisfies the condition If(x) –…

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Q: Find  f ∘ g and g ∘ f. f(x) = squere root x-8 to the power 3, g(x) = x3 + 1   (a)  f ∘ g

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Q: Find the Domain of f-1, if f(x) = 2(x – 7)² Domain: y is all real numbers Domain: x > 0 Domain: y >…

A: The range of a function f(x) is the domain of the inverse function f-1(x). The domain of f(x) is the…

Q: 3. Just Take it to the Limit For this problem, evaluate the limit if it exists, or state why a…

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Q: negative semi definite, semi definite but not positive definite, positive definite of indefinite?

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