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- Why do we restrict the domain of the function f(x)=x2 to find the function's inverse?arrow_forward2. Find the following. Let f(x)= x+1, g(x)= 2x, and h(x)=x-2.a. (h o h) (x)b. (f o g) (x)c. (g o h) (x)d. (f o h) (x)e. (g o f) (x)arrow_forwardShow that if C₁, C₂: Rd x Rd. → Problem 2. (Non-negative definite functions R are non-negative definite, then so are aC₁ + BC₂ (a, ß20) and C₁ C₂.arrow_forward
- 23) The domain of f(x) = Vx + 3 isarrow_forward1. Given the functions, f(x) a. Find Ag(4)). * and , g(x) = Vĩ. b. Find fAg(x)). c. Find g(f(4)). d. Find g(fx)). 2. Consider the functions, h(x) = 3x - 7 and k(x) = . a. Find h(k(-2)) b. Find h(k(x)) c. Find k(h(-2)) d. Find k(h(x)) 3. Consider the functions, m(x) = x + 3x and p(x) = 2x + 5, Find m(p(1)) b. Find m(p(x)) a. c. Find p(m(1)) d. Find p(m(x)) 4. Consider the functions b(x) = (x – 1) and c(x) = Vx+1, b. Find b(c(x)) a. Find b(c(9)) d. Find c(b(x)) c. Find c(b(9))arrow_forward2. Consider the functions, h(x) Find h(k(- 2)) = 3x – 7 and k(x) = . b. Find h(k(x)) a. d. Find k(h(x)) c. Find k(h(- 2) 3. Consider the functions, m(x) = x² + 3x and p(x) = 2x + 5, Find m(p(1)) b. Find m(p(x)) a. c. Find p(m(1)) d. Find p(m(x)) 4. Consider the functions b(x) = (x – 1) and c(x) = V+ 1, a. Find b(c(9)) b. Find b(c(x)) c. Find c(b(9)) d. Find c(b(x))arrow_forward
- 4. Verify that f(x) = x3 – x2 – 20x + 6 satisfies the three conditions of Rolle's Theorem on [0,5]. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. %3Darrow_forward4. Examine if functions f(x) f, (x) =x², f;(x)=x² – 2x are linearly = x, independent.arrow_forward2) a. Show that the function f(x) = A x x – B is injection function. b. Find the inverse of the function f (x) = -B × x + 5 x A Note that: A is first two-digit number (before English alphabet letter) from your college ID. B is last four-digit number (after English alphabet letter) from your college ID. For example, if your MEC ID is 16F234510, then A = 16 and B = 4510arrow_forward
- Consider the functions f, g given by f(y) = Ay, g(x) = Bx where A is m × p and B is p × n. In addition, m ‡ p, p ‡ n, and m ‡ n. Which of the following are true? g(f(y)) = B(Ay) g(f(y)) = (BA) y f(g(x)) = (AB)x f(g(x)) = A(Bx)arrow_forwardSuppose that f(z) = x² - y² - 2y + i(2x - 2xy), where z = x+iy. Write f(z) in terms of z, and simplify the result. (Hint: You may prove and use the expressions x = and y =arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell