A X(t) = [² 2x+ JUC) Find A-¹ by the Cayley-Hamilton Theorem X26) = (-₁ [SI-A)-¹(x (0) Find X(2) if X(0) = [] and (t) = [

Q: Let h(x) = f(x)g(æ). If f(x) = –3x² + 2æ – 3 and g(x) = -322 + 4x + 3, what is h' (1)? %3| Do not…

A: Given function is h(x)=f(x)g(x) where f(x)=-3x2+2x-3 , g(x)=-3x2+4x+3 f(1)=-3(1)2+2(1)-3=-3+2-3=-4…

Q: 5) Given functions T(x) = 3x – x² and S(x) = 4x – 1 find the following: a) (T • S)(x) b) (T – 5)(-)…

A: Note:  In (T o S)(x) , s(x) is input. (T-S)(x) = T(x)-S(x).

Q: Show that (a) x(t) * 8(t) = x(t)

A:

Q: Given g(x) = In(7x5 + æ), the derivative g'(x) is 5x4 35x4 +1 7x5 + I O 7z5 +x 7x +I 35x4 +1 O 35x*…

A:

Q: 4. Let f(x)= |x| and g(x) = x-3. (a) Determine the formulas for each of the related composite…

A: The composite function is defined as when the output of one function is used as the input of another…

Q: Find functions g and h such that f(x) = g(h(x)). f(x) = e4x + 2 A. g(x) = 4x+2, h(x) = ex OB. g(x)=…

A:

Q: h(x) = 1 – x – x2 (a) Express h in standard form. h(x) = %3D

A: We will solve the problem

Q: Select which function f has an inverse g that satisfies g'(1) = Of(x) = 2x³ Of(x) == x³ Of(x) = x³…

A: To find the function  that has an inverse  that satisfies .

Q: Show that: n n > (xi – x)2 > x? – n(x)2 | i=1 i=1

A:

Q: - Show that f(x)= E ƒ(x), where E is a constant and f(x)= e²x + e2x

A: