Let A, B be sets, let P, Q ⊆ A be subsets of A, and let f: A → B be an injective function. Prove that f(P) − f(Q) = f(P − Q).

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A: Given: A fixed point of a function f is a number c in its domain that satisfies f(c).

Q: 5. If x1 and x2 are two different inputs of a function f, then f is one-to-one if

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Q: f (x) = e*²+2 at x = 1 with h = 0.5

A: As no method is mentioned, I am using Taylor polynomial of order 2 for approximation.

Q: 2. define the functions f(x1, x2) = x1x2 the largest and smallest value in the set x12 + 4x22 = 8.

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Q: (d) Suppose that ƒ: P → Q and g: Q → R are functions. (i) Show that the composite function gof : P →…

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Q: 2. Evaluate the piecewise defined function at the indicated values. x2 + 4x if x s -3 Ax) = {x if -3…

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Q: Suppose that a function ƒ(x) has the property that ƒ(x1 x2) = ƒ(x1) + ƒ(x2) for any two positive…

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A: Here if a≠b then f(a)≠f(b) is equivalent as f(a)=f(b) then a=b

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Q: A TUN f: {1,2,3,4} is defined by f(1) = 6, ƒ(2) = 7, f(3) = 8, Drag the answers into the right place…

A: Given function is f:1, 2, 3, 4 → 5, 6, 7, 8 defined by f(1) = 6, f(2) = 7, f(3) = 8, f(4) = 6

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