.
Relations and Functions
Question 1. The function f : A → B defined by f(x) = 4x + 7, x ∈ R is
(a) one-one
(b) Many-one
(c) Odd
(d) Even
Answer: (a) one-one
Question 2. The smallest integer function f(x) = [x] is
(a) One-one
(b) Many-one
(c) Both (a) & (b)
(d) None of these
Answer: (b) Many-one
Question 3. The function f : R → R defined by f(x) = 3 – 4x is
(a) Onto
(b) Not onto
(c) None one-one
(d) None of these
,Answer: (a) Onto
Question 4. The number of bijective functions from set A to itself when A
contains 106 elements is
(a) 106
(b) (106)2
(c) 106!
(d) 2106
Answer: (c) 106!
Question 5. If f(x) = (ax2 + b)3, then the function g such that f(g(x)) =
g(f(x)) is given by
(a) \(g(x)=\left(\frac{b-x^{}}{a}\right)\)
(b) \(g(x)=\frac{1}{\left(a x^{2}+b\right)^{3}}\)
(c) \(g(x)=\left(a x^{2}+b\right)^{}\)
(d) \(g(x)=\left(\frac{x^{}-b}{a}\right)^{}\)
Answer: (d) \(g(x)=\left(\frac{x^{}-b}{a}\right)^{}\)
Question 6. If f : R → R, g : R → R and h : R → R is such that f(x) = x2, g(x)
= tanx and h(x) = logx, then the value of [ho(gof)](x), if x =
\(\frac{\sqrt{\pi}}{2}\) will be
(a) 0
(b) 1
(c) -1
,(d) 10
Answer: (a) 0
Question 7. If f : R → R and g : R → R defined by f(x) = 2x + 3 and g(x) = x2
+ 7, then the value of x for which f(g(x)) = 25 is
(a) ±1
(b) ±2
(c) ±3
(d) ±4
Answer: (b) ±2
Question 8. Let f : N → R : f(x) = \(\frac{(2 x-1)}{2}\) and g : Q → R : g(x) = x
+ 2 be two functions. Then, (gof) (\(\frac{3}{2}\)) is
(a) 3
(b) 1
(c) \(\frac{7}{2}\)
(d) None of these
Answer: (a) 3
Question 9. Let \(f(x)=\frac{x-1}{x+1}\), then f(f(x)) is
(a) \(\frac{1}{x}\)
(b) \(-\frac{1}{x}\)
(c) \(\frac{1}{x+1}\)
, (d) \(\frac{1}{x-1}\)
Answer: (b) \(-\frac{1}{x}\)
Question 10. If f(x) = \(1-\frac{1}{x}\), then f(f(\(\frac{1}{x}\)))
(a) \(\frac{1}{x}\)
(b) \(\frac{1}{1+x}\)
(c) \(\frac{x}{x-1}\)
(d) \(\frac{1}{x-1}\)
Answer: (c) \(\frac{x}{x-1}\)
Question 11. If f : R → R, g : R → R and h : R → R are such that f(x) = x2,
g(x) = tan x and h(x) = log x, then the value of (go(foh)) (x), if x = 1 will be
(a) 0
(b) 1
(c) -1
(d) π
Answer: (a) 0
Question 12. If f(x) = \(\frac{3 x+2}{5 x-3}\) then (fof)(x) is
(a) x
(b) -x
(c) f(x)
(d) -f(x)
Relations and Functions
Question 1. The function f : A → B defined by f(x) = 4x + 7, x ∈ R is
(a) one-one
(b) Many-one
(c) Odd
(d) Even
Answer: (a) one-one
Question 2. The smallest integer function f(x) = [x] is
(a) One-one
(b) Many-one
(c) Both (a) & (b)
(d) None of these
Answer: (b) Many-one
Question 3. The function f : R → R defined by f(x) = 3 – 4x is
(a) Onto
(b) Not onto
(c) None one-one
(d) None of these
,Answer: (a) Onto
Question 4. The number of bijective functions from set A to itself when A
contains 106 elements is
(a) 106
(b) (106)2
(c) 106!
(d) 2106
Answer: (c) 106!
Question 5. If f(x) = (ax2 + b)3, then the function g such that f(g(x)) =
g(f(x)) is given by
(a) \(g(x)=\left(\frac{b-x^{}}{a}\right)\)
(b) \(g(x)=\frac{1}{\left(a x^{2}+b\right)^{3}}\)
(c) \(g(x)=\left(a x^{2}+b\right)^{}\)
(d) \(g(x)=\left(\frac{x^{}-b}{a}\right)^{}\)
Answer: (d) \(g(x)=\left(\frac{x^{}-b}{a}\right)^{}\)
Question 6. If f : R → R, g : R → R and h : R → R is such that f(x) = x2, g(x)
= tanx and h(x) = logx, then the value of [ho(gof)](x), if x =
\(\frac{\sqrt{\pi}}{2}\) will be
(a) 0
(b) 1
(c) -1
,(d) 10
Answer: (a) 0
Question 7. If f : R → R and g : R → R defined by f(x) = 2x + 3 and g(x) = x2
+ 7, then the value of x for which f(g(x)) = 25 is
(a) ±1
(b) ±2
(c) ±3
(d) ±4
Answer: (b) ±2
Question 8. Let f : N → R : f(x) = \(\frac{(2 x-1)}{2}\) and g : Q → R : g(x) = x
+ 2 be two functions. Then, (gof) (\(\frac{3}{2}\)) is
(a) 3
(b) 1
(c) \(\frac{7}{2}\)
(d) None of these
Answer: (a) 3
Question 9. Let \(f(x)=\frac{x-1}{x+1}\), then f(f(x)) is
(a) \(\frac{1}{x}\)
(b) \(-\frac{1}{x}\)
(c) \(\frac{1}{x+1}\)
, (d) \(\frac{1}{x-1}\)
Answer: (b) \(-\frac{1}{x}\)
Question 10. If f(x) = \(1-\frac{1}{x}\), then f(f(\(\frac{1}{x}\)))
(a) \(\frac{1}{x}\)
(b) \(\frac{1}{1+x}\)
(c) \(\frac{x}{x-1}\)
(d) \(\frac{1}{x-1}\)
Answer: (c) \(\frac{x}{x-1}\)
Question 11. If f : R → R, g : R → R and h : R → R are such that f(x) = x2,
g(x) = tan x and h(x) = log x, then the value of (go(foh)) (x), if x = 1 will be
(a) 0
(b) 1
(c) -1
(d) π
Answer: (a) 0
Question 12. If f(x) = \(\frac{3 x+2}{5 x-3}\) then (fof)(x) is
(a) x
(b) -x
(c) f(x)
(d) -f(x)
