Alariha N
N VINJEE
FUNCTIONS
Assignment
QI The domain ofthe function f(x) =
sin (3- X)is
.n(|x|-2)
(1) [2, 4] (2) (2, 3) U (3,4] (3) (2, o) (4) (-o,-3)U[2, o)
Q.2 Domain ofthefunction log |x²-9| is
(3) R-{-3,3} (4) None ofthese
()R (2) R-(-3, 3]
Q.3 The domain of the function f(x)=|log; is
|sin x |
(1) R-{2nn, ne I} (2) R- {nt, n e I}
(3) R-{- I, N} (4)(-o, oo)
Q.4 The domain ofthe function f(x) =log(Vx -4 +d6-x) is
(2) (-o, 6] (3) (4, 6] (4) None of these
(1) [4,o)
3
Q.5 Domain of definition ofthefunction f(x) =4-x?-+log,o(x -x), is
(1) (1,2) (2)(-1, 0) v(1,2)
(3) (1, 2) w (2, o) (4) (-1,0) U(1,2)u (2, o)
X-3
Q.6 Domain of the function f(x) =
(x-1)Vx?-4
()(1,2) (2) (-0,-2) U (2, o)
(3) (o,-2) U(1, o) (4)(-o, oo)u{1, +2}
Q.7 The domain of thefunction f(x) =sin{(1 +e)} is
(2) (-1,0] (3) [0, 1] (4)(-o, co)
Q.8 The domain ofthe function Jlog(x-6x +6) is
()(-o, co) (2) (-,3-3)u(3+5,a)
(3)(- o, 1]v[s, o) (4) [0, co)
Q.9 For 9 > ,then value of f(0)= sec0 +cos?0 always lies in the interval
3
(1)(0,2) (2) [0, 1] (3) (1, 2) (4) (2, co)
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Q.10 The rangeofthe functiont )=tm
(2) (0, I (3)(3, V3) (4)1V3,3]
(1) [0, 3)
Q.ll The rangeoffx)=scc cos
(2) [1, o)
()[ 21
(2) (-/2,-1]v[, 2] (4)(-, -1]v[l, o)
x*+*+2
Q.12 Range ofthe function fx) = x*+x+l ;XERis
()(1, o) (2) (1. 11] (3) (1, 773] (4) (1, 7/5]
Q.13 The range offx)=cos x- sinx is
()41, ) (2) [-1, 1) (4) -V2, V
Q.14 Range of the function
2-sin 3x
()[1, 3] (3) (1,3)
Q.1S The value ofb and cfor which the identity f(x +1)-f(x) =8x +3 is satisfed, where f(x)=bx² +cx +d.
are
(1) b=2, c=1 (2) b=4, c =-1 (3)-b=-1,c=4 (4) b=-1, c = 1
Q.J6 The function f: R-’Ris given byf(x) =*-1is
(1)Aone-one function (2) An onto function
(3) Abijection (4)Neither one-one nor onto
Q.17 The function f: R ’R defined as f(x) =(x-1) (x-2) (*-3) is
(1) One-one but not onto (2) Onto but not one-one
(3)Both one-one and onto (4) Neither one-one nor onto
Q.18 For real x, let f(x) =x² + 5x + 1, then
(1) fis onc-one but not onto R (2) fis onto R but not one-one
(3) fisone-one and onto R (4)fis neither one-one nor onto R
Q.19 Set Ahas3 elements and set Bhas 4 elements. the number ofiniection that can be
defined fromAto B
(1) 144 (2) 12 (3) 24 (4) 64
Q.20 1fR denotes the set ofall real numbers then the function f:
(1)One-one only R’R defined as fx)- (x] will be
(3) Both one-one and onto (2) Onto only
(4) Neither one-one nor onto
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2x
(x) = tan-! ,then fis both one-one and onto when
Q.21 Let f:(-1, 1)’ B, bc afunction defined by
Bis the interval
o)
e-e
+2 is given by
Q.22 The inverse ofthe funciton f(x) = e+e
\/2 \/2
1/2
(1) log. (3) log,
Q.23 Which ofthe following funtion has inverse function
(4) (x) =x, xs0
(2) f(x) = x² for all x (3) f(×) =x', x>0
(1)f(X)x-l 10-10-N
Q.24 The inverse ofthe function 10 +J0-xIS
(4) None ofthese
3)
Q.25 Let (x) =sinx+cos x, g(x) =x-1. Then g(f(x)) is invertible for xE
Q.26 The function (x)=s
(1) Even function (2) Odd funct ion
(3) Neither even nor odd (4) Periodic function
x'+1|
is a odd function then the value of parametric P is
Q.27 Ifg:(-2, 2]-’R where g(x) = +tanx + P
(1)-5 <P<s (2) P<s (3) P>s (4) None ofthese
Q.28 1ffx) is periodic funciton with period Tthen the function (ax +b) where a>0, is periodic with period
(1) T/b (2) aT (3) bT (4) T/a
Q.29 Supposethat g(x) =1+ x and flg(x) =3 +2/x tx, then f(x) is
(1) 1+ 2x? (2) 2 + x² (3) I+x (4)2 + x
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-1, x<0
thenfor allx, f(g(x) is equalto
fx)=0,x=0,
g(x) =1 +x- [x] and
Q.30 Let 1,x>0
(3) f(x) (4) g(x)
(2) 1
(1)x ff(x)] =
n is a positive integer, then
x")ln, where a>0 and (3)x (4) None ofthese
Q.31 Iff(x)=(a - (2)x²
(1) x
function 'f' satisfies the relation
Q.32 Iapolynomial
f(x) and f(10) = 1001,
log, 1+
log,((0) =log,2+
then the value of f(20) is (3) 8001 (4) 16001
(1) 2002 (2) 7999
mand Mrespectively then
maximum values of fx) =2<x -1|+|x+3|-3}x -4 are
Q.33 Ifminimumand
(m+ M) equals (3) 2 (4)3
(1)0 (2) 1
granhs
that
be defined as f(x) =4x*-16x +22 and g(x) s a functionsuch cqual to
Q.34 Let f: (-o,2]’6, co) image of cach othcr with respect to lne X-y=0, then g10) is
of fx) and g(x) are miror (3) 3 (4)4
(1)1 (2) 2
2x +1)
functional equation f(x) + 2 1 , =3x, x * 2,
the
Q.35 Let f be a function satisfying
thenfind the vaeof r
greatest integer and fiactional part functions respectively
Q.36 Let fx) = cos{x} where [y]and {y} denote
2x?-3x(k +1) +k(3k +1). If glf(x))<0xeRthen find the number ofintegral values
and g(x) =
of k.
Q.37 Solve the following problens from (a) to (e) on functional equation.
f(r)1+f(x)) =-f()10ral
(a) The functionf(x) defined on the real numbers has the property that
compute the value o1 y()
xin the domain off. Ifthe number 3is in the domain and range of f, the value of f(21).
(b) Supposef is areal function satisfyingf(x+f(x)) =4f(x) andf(1) =4. ind
positivenumbers xandyand
(c) Let 'ffbe afunction defincd fromR*’R*.Jf f(xy))'=xfy} for all
f(2)=6, fnd the value off(50). Page#4
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() Let f(x) be a function with two properties
f(0) = 2.
for any tworeal number xand y, f(x+y)=x+fy) and
Fnd the value of f(100).
vaue of f(300).
(e) Letf be a function such that f(3)= landf(3x) = x+f(3x-3) for allx Then fnd the
ax+ bx +a+d-15x -1
(K=0).
() Suppose that f(x) is a function ofthe form f(x) =
If f(5) = 2then fird the value of f(-5).
Q38(0) Let g:R’R be defned as g(x) = e-ef
2
e(f(*))=x, then End the value of f 2e
Let f be a real vahed invertible function such
that f x-3-5x -2, x*2. Fod f15).
x-2,
