Problem 3. Let F and G be two functions defined as { and F(x)= sin - 0, " x G(z) = { ₁,² if x # 0, if x = 0. -F(x), if x 0, if x = 0. Show that both F and G have the Intermediate Value Property, yet F+ G does not. Thus the class of functions with IVP is not closed under addition

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A: Using Mean Value Theorm.

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A:

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Q: If h(x)  =   x  +  1     if x˂  -1                               2  + 2x    if x ≥  -1        Find…

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Q: Consider the functions f(x)= [x²-9 x*-1 2x ; x=-1 and (3x+2 g(x) = { x=-1 Define the new function…

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Q: o Function f₁: R → R is defined by f₁ (x) = (x + 1)². • Function f2: R → R is defined by f2(x) =…

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Q: Where is the function f(x) = if x 0 removable discontinuity? Is it a jump discontinuity?

A: A jump discontinuity occurs when right and left limit exists but are unequal .

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A: Let's solve for inflection points at which points.

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Q: . Solve the following a) Simplify f(x+h) - f(x) where f(x) = x^2-2x b) If f(x) = (x-2) (x^2-1),…

A: f(x)=x2-2x Now we find out f(x+h). Replace x with x+h f(x)=x2-2xf(x+h)=(x+h)2-2(x+h)=x2+2xh+h2-2x-2h…

Q: the inverse function of f(x) = ax is x+c hat is the value of a + b + c? +C= f-¹(x)= 8x - 7 .-x+3'

A: Topic:- algebra and calculus

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Q: If f(28) = 16 and f is one-to-one, what is f'(16)? f (16) =

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Q: By using False Position for f(x) = x3 - 4x +4 (XL=-3; xU=2) xr will replace

A: This is interesting question but before the solution we must know about the  false position method…