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ELEMENTS OF MODERN ALGEBRA
- If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?arrow_forward26. Let and. Prove that for any subset of T of .arrow_forward2 For 1 X+ 1 and g(x)=, find b. the domain of fo g a. (fo g)(x): a. (fo g)(x)= (Simplify your answer) AEneriou ansernine ansyer pex and inen erck 1 remainine enitr copyright S 2019 Pear search Xarrow_forward
- In the three envelopes shown, the statements on one of the three are both true, the statements on another are both false, and the remaining envelope has one statement that is true and one that is false. Which envelope contains the formula?arrow_forwardRefer to the following functions: p(x) = x2 + 2x – 15 x+1 q(x) = X-3 r(x) = v7-x Which of the following statement/s is or are true? i. The composite function r q is defined for all x <7. Note:r•q=r[q(x)] ii. The resulting function of the product of p and q is defined for any real number x. ii. The difference quotient --2 is defined for any real number h except 0. 4. O i only ii only iii only O i, ii, and iiiarrow_forwarda. Let X = {2, 4, 6} and Y = {a, b, c, d'}. Define g : X→ Y by the following arrow diagram. X 2 4 bo g The domain of this function is (A) {a,b,c,d} (B) {b} (C) {2,4,6} (D) All real numbers b. The codomain of this function is (A) {b} (B) {a,b,c,d} (C) {2,4,6} Y a b C darrow_forward
- Determine b so that f(x) is continuous if O 8 x + 6 f( x ) = 0 O 2 x2 + b x +10 x > 6 b =arrow_forward3. Let f(x) = x² + 3 and g(x) and [3, 0), respectively. = Vx – 3 be functions defined on [0, 0) i. Draw the graphs of f and g on the same plane with the equation y = x. (Use different colors for each graph, if possible, and label the graphs properly.) ii. Give an argument about the relationship of the functions f and g. (Write it in paragraph form with at least 2 sentences.)arrow_forward. Consider the following pair of functions: f: Z → Z defined by f(x) = 3x - 2 g: N→→ Z defined by g(n) = 2 - n a. Determine whether fog is well-defined and write (fog)(x) explicitly if it is well-defined. b. Determine whether g of is well-defined and write (gof)(x) explicitly if it is well-defined.arrow_forward
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