Define f : R → R and g : R → R by the rules f(x) = 3.x – 2 for all x E R and g(x)= x² +3 for all x E R. (i) Is f one-to-one? Prove or give a counterexample. (ii) Is g one-to-one? Prove or give a counterexample.

Q: Q2: (a) Determine which of these functions are injective, surjective, and bijective. The function f…

A: a:Given are the following functions:i fx=2x+1ii fx=exiii fx=x3-3xTo find that the following…

Q: Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing…

A: f(x) = 5x4 - 8x5∫f(x) = ∫5x4 - 8x5 dxF(x) = 5  x55 - 8 x66 + CSubstitute x = 0 F(0) = 0 - 0 + C 2=C…

Q: If f : R → R is defined by                      f(x) = x2– 3x + 2, find f (f(x)).

A: Given,

Q: Od. The function f: [0,00)→ R given by f(x)=x¹/2 is Lipschitz. e. The function f: [0,∞) → R given by…

A: Lipschitz Function: Let A⊂R, and f(x):A→R, then f(x) is called Lipshitz Function on A if ∃k>0,…

Q: Consider the functions from R to R defined by f(x) = x² + 3x - 2 and g(x) = 2x+4 a. What is fog(x)?…

A:

Q: If f(x) = x + /2 – x and g(u) = u + v2 – u , is it true that f = g?

A:

Q: Consider the function f(x) х — 2 х — 4*

A: The solution are next step

Q: (b) Let the function f: R → R defined by 3x for x > 3 2x2 + 3 for - 2 < x< 3 3 x? – 7 for x<-2 f(x)…

A:

Q: or f(x) = Vx – 1, g(x) = x² - 3, find fog and go f. Give the domain of each mposition

A: Given f(x) = x-1           g(x) = x2-31) f∘g(x) = f(g(x))                   =(x2-3)-1…

Q: Suppose that f: R20 R20 is defined by f(x) = x². What can we say about f? →

A: Sol:- Given :- f:R≥0→R≥0It is clear that doamin of Function fx ≥0 and Range of function fx is also…

Q: Which is true for the function f(x) = x³ + x – 1? O a. f(x) has a root in (0, 1). cross out O b.…

A: For simplicity, we will be plotting the function to get the roots and the intervals at which it is…

Q: Function f and g are defined for xE R by f:x→ 2x + 5 Find x such that (fog)(x)=9. and g:→ 8x-2

A: Given two real functions are f(x)=2x+5g(x)=8x-22

Q: 1. Let f(x) = x² + 1. %3D (a) Compute f(0), f(-1), f(1/2), and f(/2). (b) For what values of x is it…

A:

Q: 6.) Find f/g and its domain. т — 2 3 f(x) g(x)

A: To Find f/g and its domain. f(x) = 3x,  g(x) = x-2x

Q: (d) Are X1 and X2 independent? Justify. (e) Compute E(X1) and V(X1).

A:

Q: Let f(x) = and g(x) = 2х -1 Compute (f o g)(x) and determine the domain in x-2 interval notation.

A:

Q: Suppose that f(x) is a function such that f(5) = 0 and f(x) is positive for all x 5. What is the…

A: Find the domain of function g(x)

Q: Let T: P, → R? be the function defined by the formula T(p(x)) = (p(0), p(1)). Find T(5,4). Select…

A: We will assume a linear polynomial whose image is given to us. Now we will use the definition of T…

Q: Use the function f(r) given below to answer the questions that follow. f(r) = – 2(r+1)(r – 3) (r –…

A: The given function f(r)=-2r+1r-33(r-1)

Q: 1 Consider f(x) x – 16 a. Compute: f(a) = b. Compute and simplify: f(a + h) = c. Compute and…

A:

Q: Find the set of values of b so that the function f:R→R given by 21-4b - b? f (x) = | 1- x³ +5x + a,b…

A: B belongs to [2,3]

Q: 3. For the Functions f (x) – 3x – 4 and g (x) = x+2, find the following and detemine the domain in…

A:

Q: Let f: RR, f(x) = -2x+5 and g: RR, g(x) = − x Find (gof) -¹(x) (select the correct answer) ○ x+5 2…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.