الصفحة الرئيسيةchapter-4 Chapter 4 : Functions - Multiple Choice Questions သူရိန်မင်း الخميس, أغسطس 05, 2021 0 မှန်သော အဖြေကို ရွေးပေးရန် ဖြစ်ပါသည်။ If A={a,b,c}, then n(A×A)= A. 3 B. 6 C. 9 D. 12 Explanation A={a,b,c}A×A={(a,a),(a,b),(a,c), (b,a),(b,b),(b,c), (c,a),(c,b),(c,c)}∴n(A×A)=9Note that n(A×A)=[n(A)]2 Given that A={a}, then A×A= A. {a} B. {(a,a)} C.{a,a} D. a2 Explanation A={a}A×A={a}×{a}={(a,a)} product sets ၏ အစု၀င်များကို orderd pair (x,y) ပုံစံဖြင့်ရေးရသည်။ Given that f(x)=x2+3x+1. If f(a)=314 where a>0, then what is the value of a ? A. 32 or 92 B. −32 or 92 C.−92 or 32 D. 32 Explanation f(x)=x2+3x+1f(a)=314a2+2a+1=3144a2+12a−27=0(2a+9)(2a−3)=0a=−92 (or) a=32 Since a>0, the correct solution is a=32. What is the domain of f(x)=1x2−4. A. R∖{−2,2} B. R∖{4} C. R D. ∅ Explanation f(x) is not defined when x2−4=0 x2=4 x=±2 ∴ dom (f)=R∖{−2,2}. Given that A={x∣x>0,x∈R} and function f:A→R and g:A→R ane defined as f(x)=x−2 and g(x)=x2−4x+2. Which of the following is(are) true? I. f(2)=g(2) II. f=g III. f≠g A. I only B. II only C.I and II only D. I and III only Explanation dom(f)=dom(g)=A={x∣x>0,x∈R} ∴dom(f) and dom(g) are the set of positive real nembers. f(x)=x−2 and g(x)=x2−4x+2=(x−2)(x+2)x+2=x−2 when x≠−2 Since −2∉A, we can say f(x)=g(x) for all x∈A The graph of the function y=ax2+bx+c when a=0 is A. straight line B. parabola C. circle D. ellipse Explanation Generally y=ax2+bx+c is a quadratic function. But when a=0,y=bx+c is a linear function and the graph is a straight line. What is the equation of horizontal asymptote of the curve y=3x−1+2. A. y=2 B. y=3 C. x=1 D. x=−1 Explanation We have known that the graph y=kx−p+q has horizontal asymptote y=q and vertical asymptote x=p. ∴ The horizontal arympatote of y=3x−1+2 is y=2. The furction f(x)=3x−1+2 is not defined when A. y=2 B. y=3 C. x=1 D. x=−1 Explanation A rational function is not defined when its denominator is equal to zero. ∴f(x)=3x−1+2 is not defined when x−1=0 or x=1, The vertical asymptote of the graph of function y=−3x+4x−2 is A. x=2 B. x=−2 C. x=43 D. y=−3 Explanation We have known that the graph y=kx−p+q has horizontal asymptote y=q and vertical asymptote x=p. y=−3x+4x−2=−2x−2−3 ∴ The vertical asymptote of y=−3x+4x−2 is x=2. Which of the following is one to one? A. f(x)=x2 B. f(x)=|x| C.f(x)=x4−1 D. f(x)=x3+3 Explanation See: Definition of one to one furction Chapter (4), Section (4.3.2) If f−1(x)=x−32, then f(x)=… A. x−3 B. 2x−3 C. 2x+3 D. x−23 Explanation f−1(x)=x−32 Let f(x)=y, then f−1(y)=x y−32=x y=2x+3 ∴f(x)=2x+3 Given that f(x)=42−3x, then the domain of f−1 is A. {n∣x≠32,x∈R} B. {x∣x≠23,x∈R} C. {x∣x≠−23,x∈R} D. {x∣x≠0,x∈R} Explanation f(x)=42−3x If f−1(x)=y then f(y)=x 42−3y=x 2−3y=4x 3y=−4x+2 y=2x−4x f−1(x)=2x−43x ∴f−1 exists when x≠0. If f(x)=3x−12x+1, f−1(1)=… A. 0 B. 1 C. 2 D. 3 Explanation f(x)=3x−12x+1 f−1(1)=a f(a)=1 3a−12a+1=1 3a−1=2a+1 a=2 ∴ f−1(1)=2 The function f is given by f(x)=10x−2, then f−1(2)=⋯ A. 88 B. 0.4 C. ln4 D. log104 Explanation f(x)=10x−2 Let f−1(2)=a f(a)=2 10a−2=2 10a=4 a=log104 ∴ f−1(2)=log104 Given that f(x)=x2, what is the domain of f for which f−1 exists? A. {x∣x≠0,x∈R} B. {x∣x>0,x∈R} C.{x∣x≥0,x∈R} D. {x∣x<0,x∈R} Explanation f−1 exists if and only if f is a one to one function. f(x) is one to one only when x≥0. ∴dom(f)={x∣x≥0,x∈R}. If f(x)=x2 and g(x)=2x,(f∘g)(−12)=… A. 1 B. 0 C. −1 D. 14 Explanation f(x)=x2 g(x)=2x (f∘g)(−12) =f(g(−12)) =f(2(−12)) =f(−1) =(−1)2 =1 If f(x)=x2 and g(x)=2x+1x−4, what is the domain of g∘f ? A. {−2,2} B. R∖{4} C. R∖{±2} D. R Explanation f(x)=x2g(x)=2x+1x−4(g∘f)(x)=g(f(x))=g(x2)=2x2+1x2−4(g∘f)(x) exists when x2−4≠0x2≠4x≠±2∴ dom(g∘f)=R∖{±2} If g(x)=x+22x−1 and h(x)=2x, what is the range of g∘h? A. R B. ∅ C.R∖{2} D. R∖{12} Explanation g(x)=x+22x−1h(x)=2x(g∘h)(x)=g(h(x))=g(2x)=2x+24x−1=5/24x−1+12∴ran(g⋅f)={y∣y≠12,y∈R} The function f:A→B is onto function then the range of f is A. A B. B C. subset of A D. subset of B Explanation A function f is onto function when range of f= codomain. If f is a function an a set A={1,2,3,4,5} such that f={(1,2),(2,3),(3,4),(4,x),(5,5)} is a one to function, then x=… A. 5 B. 3 C. 2 D. 1 Explanation To be one to ove furction f, A must be related with 1. Submit answers Your Score: စာဖတ်သူ၏ အမြင်ကို လေးစားစွာစောင့်မျှော်လျက်!