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Chapter 4 : Functions - Multiple Choice Questions

မှန်သော အဖြေကို ရွေးပေးရန် ဖြစ်ပါသည်။

  1. If A={a,b,c}, then n(A×A)=
    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
  2. Given that A={a}, then A×A=
    Explanation
    A={a}A×A={a}×{a}={(a,a)}

    product sets ၏ အစု၀င်များကို orderd pair (x,y) ပုံစံဖြင့်ရေးရသည်။
  3. Given that f(x)=x2+3x+1. If f(a)=314 where a>0, then what is the value of a ?
    Explanation
    f(x)=x2+3x+1f(a)=314a2+2a+1=3144a2+12a27=0(2a+9)(2a3)=0a=92 (or) a=32
    Since a>0, the correct solution is a=32.
  4. What is the domain of f(x)=1x24.
    Explanation
    f(x) is not defined when
    x24=0
    x2=4
    x=±2
    dom (f)=R{2,2}.
  5. Given that A={xx>0,xR} and function f:AR and g:AR ane defined as f(x)=x2 and g(x)=x24x+2. Which of the following is(are) true?
    I. f(2)=g(2) II. f=g III. fg
    Explanation
    dom(f)=dom(g)=A={xx>0,xR}
    dom(f) and dom(g) are the set of positive real nembers.
    f(x)=x2 and g(x)=x24x+2=(x2)(x+2)x+2=x2 when x2
    Since 2A, we can say f(x)=g(x) for all xA
  6. The graph of the function y=ax2+bx+c when a=0 is
    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.
  7. What is the equation of horizontal asymptote of the curve y=3x1+2.
    Explanation
    We have known that the graph y=kxp+q has horizontal asymptote y=q and vertical asymptote x=p.
    The horizontal arympatote of y=3x1+2 is y=2.
  8. The furction f(x)=3x1+2 is not defined when
    Explanation
    A rational function is not defined when its denominator is equal to zero.
    f(x)=3x1+2 is not defined when
    x1=0 or x=1,
  9. The vertical asymptote of the graph of function y=3x+4x2 is
    Explanation
    We have known that the graph y=kxp+q has horizontal asymptote y=q and vertical asymptote x=p.
    y=3x+4x2=2x23
    The vertical asymptote of y=3x+4x2 is x=2.
  10. Which of the following is one to one?
    Explanation
    See: Definition of one to one furction Chapter (4), Section (4.3.2)
  11. If f1(x)=x32, then f(x)=
    Explanation
    f1(x)=x32
    Let f(x)=y, then
    f1(y)=x
    y32=x
    y=2x+3
    f(x)=2x+3
  12. Given that f(x)=423x, then the domain of f1 is
    Explanation
    f(x)=423x
    If f1(x)=y then
    f(y)=x
    423y=x
    23y=4x
    3y=4x+2
    y=2x4x
    f1(x)=2x43x
    f1 exists when x0.
  13. If f(x)=3x12x+1, f1(1)=
    Explanation
    f(x)=3x12x+1
    f1(1)=a
    f(a)=1
    3a12a+1=1
    3a1=2a+1
    a=2
     f1(1)=2
  14. The function f is given by f(x)=10x2, then f1(2)=
    Explanation
    f(x)=10x2
    Let f1(2)=a
    f(a)=2
    10a2=2
    10a=4
    a=log104
     f1(2)=log104
  15. Given that f(x)=x2, what is the domain of f for which f1 exists?
    Explanation
    f1 exists if and only if f is a one to one function.
    f(x) is one to one only when x0.
    dom(f)={xx0,xR}.
  16. If f(x)=x2 and g(x)=2x,(fg)(12)=
    Explanation
    f(x)=x2
    g(x)=2x
    (fg)(12)
    =f(g(12))
    =f(2(12))
    =f(1)
    =(1)2
    =1
  17. If f(x)=x2 and g(x)=2x+1x4, what is the domain of gf ?
    Explanation
    f(x)=x2g(x)=2x+1x4(gf)(x)=g(f(x))=g(x2)=2x2+1x24(gf)(x) exists when x240x24x±2 dom(gf)=R{±2}
  18. If g(x)=x+22x1 and h(x)=2x, what is the range of gh?
    Explanation
    g(x)=x+22x1h(x)=2x(gh)(x)=g(h(x))=g(2x)=2x+24x1=5/24x1+12ran(gf)={yy12,yR}
  19. The function f:AB is onto function then the range of f is
    Explanation
    A function f is onto function when range of f= codomain.
  20. 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=
    Explanation
    To be one to ove furction f, A must be related with 1.
  21. Your Score:

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