4. Determine if the following functions are onto. Explain why. f:R R f(x) = x³ + 200 •f:R → R •f: Z→R ● f(x)=x+2 . f(x) = x + 2 f:Z-Z f(x)=x-3 f: R+ → R f(x)=√x

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

A: Given,

Q: 4. Let f(x)=1+x³-x. Find an x-value that makes f(x) 0.

A:

Q: 1. Find the following for the function f(x, y) = 3x³y² - 5x + 26y - 9.

A:

Q: Evaluate the following functions. 1. Iff(x) = x? - 2x +7, find a) f(0), b) f(2y+1). 2. If F(y) = vty…

A: Given:1. fx=x2-2x+72. Fy=yy-32

Q: 5. Let f : R -→ R be defined by f(x) = 2x +9. Find a formula for f-1.

A: We need to find the inverse function of the real valued function f(x)=2x+9

Q: Q7. Check if the following functions are Orthogonal or not? fi(x) = x°, f2(x) = x² + 1 [-1, 1] on…

A:

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: Find the domain of the function defined by f(z) = iz – iz Select one: O a. Re(z) # 0 O b. Im(z) + 0…

A:

Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x +1 on [-1,3]

A:

Q: f(x,y) = x²y + 2xy² + 5y³

A:

Q: Find R2,2(x) for f(x)

A: Given, fx=ln1+xx. We have to find R2,2x for fx. Here, R2,2x is called as Pade approximation. Pade…

Q: Show that the following function is nowhere analytic. f(2) = 2xy + i(x² – y³) %3D

A: Function is said to be analytic at a point if there is a nbd of the point such that f is…

Q: .Let f, g andh are three functions defined as below : f: R>Rf(x) = 4x² – 4, - g. R→R8 (x) = V-5x+…

A: Given  f(x) = 4x2-4g(x) = -5x+1h(x) = 2x-5   a) fog(x) = f(g(x)) = f(-5x+1) = 4-5x+12-4 =…

Q: . Show that the function f: R→ R defined as f(x) = 13x − 15 is one-to-one.

A:

Q: Let X-(3, 4, 6, 8). Determine whether or not the relation R = {(x, f(x)) :x - X, f(x) %3D = x2 + 1}…

A: Solution is given as: Hope the answer is helpful.

Q: Let f (x) = 2x + 3. Compute R6 and L6 over [0, 3].

A:

Q: 1. Decide if there is an analytic function f (x + iy) whose real part satisfies Re(f) = xe".|

A: Given problem: To decide analytic function fx+iy whose real part satisfies Ref=xey.

Q: If f(z) is analytic function and u(x,y) = x3 - 3xy find f(z) %3D

A: Given that the real part of the analytic function f(z) is, u(x,y) =x3-3xy To find the analytic…

Q: 4. Find the functions f(x), g(x),h(x) that satisfy: f(g(h(x))) = 2.

A: A composite function is created when one function is substituted into another function .

Q: Compute the following values for the given function. f(x, y) = 4x2 + 2xy – 7x + 4 f(1, 2) %3D f(2,…

A:

Q: 1. Identify and sketch the domain of f(x, y) = √y² + 4x + 2 In(1-x² - y²)

A: