For each statement, either prove that it is true or come up with a counter example N(ATA) = N(A) ● • C(AAT) = C(A) ● rank(ATA) = rank(AAT) • rank(ATA) = rank(A)

Q: Please prove 2(b)(iv)>(v)

A:

Q: Given f(x) = 23 10x, evaluate the following. (a) (f of-)(42) = (b) (f o f)(40) = %3D

A: First we will calculate the inverse of f. Then see that the composition of f and f inverse works…

Q: Find (f + g)(x)

A: we have to apply composition property to solve given function please note: we are only supposed to…

Q: Let g(x)=31-x. Compute: a) g(2.3) b) g(2) c) g(-1)

A: Given that

Q: | In(vE + 5)dt

A: Given: I=∫lnt+5dt  ……1

Q: If g(a)= b and f(b) = c, then explain how to find (f og) (a)

A: Given g(a)= b ......(1) f(b) = c .....(2)

Q: Given the functions f(x) = x? - 3 and g(x) = 2x + 1, find... a) f(g(x)) b) g•f(x) c) d) gog(x) e)…

A:

Q: f (x) = x²ex3-I

A: Given:        f(x) = x2 ex3-1

Q: 2 fax) = 2 + 3x-xª for f(x+1)

A:

Q: Given the functions f (x) = 3x + 5 = (x) 6 g (x) = 4 – x2 and h (x) = = 1 *, find each of the -…

A:

Q: How can you apply the chain rule in calculus 3 with multivariable calculus

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Q: If f(a, b) = eab (ab + a), show that fûû(a, b) — àƒÂ(a,b) = a²eab

A: We can solve this as follows:

Q: fg)(x)=  f(x)=3x−8 and g(x)=x2+16x+63 Use “U” to indicate the union of intervals.

A:

Q: FInd the following. (0, 1), v = (5, –2) u = (a) |삐 (b) ||v|| (c) |u + v|| (d) (e) u + v (f)

A:

Q: If (A) -71,then (A)] = ...

A: I have appended the formula used in the solution part.

Q: for f(x) = (x-1)3 and g(x) = 1 - 4x, find the following  a) (f o g)(x) b) (g o f)(x) c) f(f(x))…

A: (fog)(x) = f[g(x)].

Q: EVALUATE

A: ∫ x-3x-1+x2dx

Q: Let fé)--을(t)6. Eveluate f(-8) %3D f68)= ? %31

A:

Q: Let f (x) = 1(1 2 2 +4. Evaluate f(-8). f(-8) = Number

A: Given f(x) = -½(½)x + 4 We have to find f(-8)

Q: Show that * y = (y² – r*)(2² – x*)(2² – y³)

A:

Q: Use algebraic manipulation to prove that (x + y) · (x + ) = x

A: We need to prove that:Solving the Left Hand Side,Now, right Hand side,

Q: If f(14)=27, find f-1(27)

A: If f(x) = y is any function and f is one-one then, => f-1(y)=x

Q: For u(x) = 4x2 - x + 5 and v(x) = 2x + 4, which of the following is correct? a) (u – v)(2) = 11 b)…

A:

Q: f(x) 3* [(x+1) Sind 27x fx-2)

A: Givenf(x) = 3x27xexpress all the terms in 3 ( because 27=33) f(x) = 3x33x = 3x-3x= 3-2x = 132xTo…

Q: APQR = R R(R(AABC)) Given the fact that the coordinate plane below, which single-transformation and…

A: Given: Triangle ABC…

Q: Let A = B = C = {x 1 x is a real number}. Let f: A → B and g: B → C be defined as follows: f(a) 2a…

A:

Q: Evaluate f (z) = 3z² – 5x for f (-2) O 2 O 2 O - 22 O 22

A: We have to find the value of function