True or false: Let f: [0, 1] → R be a function with f(0) > 0 and f(1) < 0. Then, for all v E (f(0), f(1)) there exists c € (0, 1) with f(c) = v. Select one: True False

Q: Q7; Functions (a) Prove that the function f : Z4 → Z12 given by f(T) = [3x] is well %3D defined.

A: we need to prove homomorphism

Q: Let L(x) be the linearization of an arbitrary function f about c. Assume that f is concave down in…

A:

Q: (b) Define a function F:F: R XR → R XR as follows: For all (x, y) ERXR, (F(x, y) = (2x + y, 2x - y)…

A:

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) &lt; 0 then the function f(x)…

Q: Show that the following relations are not functions on R. a) ƒ = {(x, y) = RxR | y=x/(x² −7x+12)}

A: Given function. y=xx2-7x+12 is not define for x2-7x+12=0 =&gt; (x-3)(x-4)=0

Q: Evaluate L{f(t)} for if 0 < t,t + 1,t # 2 if t = 1 1 (i) f(t) = 3 -3 ift = 2 (ii) f(t) = 1 2t +1 if…

A:

Q: Prove that for any function f : X → Y and for any subsets Y₁ and Y₂ of Y, ƒ¯¹(Y₁ NY₂) = ƒ¯¹(Y₁) Ñ…

A:

Q: Let the function f(x) be given as follows: ax + b, x<1 f(x) = ; lt +x + 1, x 21 Employ appropriate…

A: is differentiable. Therefore, we have, RHD=LHD=f(x) Now,