Exercise 5.10 - Chapter 5 - Differential Calculus - 11th Business Maths Guide Samacheer Kalvi Solutions

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Exercise 5.10

Text Book Back Questions and Answers

Question 1.
If f(x) = x² – x + 1 then f(x + 1) is:
(a) x²
(b) x
(c) 1
(d) x² + x + 1
Answer:
(d) x² + x + 1
Hint:
f(x) = x² – x + 1
f(x + 1) = (x + 1)² – (x + 1) + 1
= x² + 2x + 1 – x – 1 + 1
= x² + x + 1

Question 2.

(a) -1
(b) 2
(c) 5
(d) 7
Answer:
(c) 5
Hint:

f(5) = 5² – 4(5) = 25 – 20 = 5
[For x = 5 take f(x) = x² – 4x]

Question 3.

(a) 2
(b) 5
(c) -1
(d) 0
Answer:
(a) 2
Hint:

f(0) = 0 + 2 = 2
[For x = 0 take f(x) = x + 2]

Question 4.

Question 5.
The graph of the line y = 3 is:
(a) Parallel to x-axis
(b) Parallel to the y-axis
(c) Passing through the origin
(d) Perpendicular to the x-axis
Answer:
(a) Parallel to x-axis
Hint:

Question 6.
The graph of y = 2x² is passing through:
(a) (0, 0)
(b) (2, 1)
(c) (2, 0)
(d) (0, 2)
Answer:
(a) (0, 0)
Hint:

y = 2x²
Put x = 0, y = 0 the equation is satisfied.

Question 7.
The graph of y = e^x intersect the y-axis at:
(a) (0, 0)
(b) (1, 0)
(c) (0, 1)
(d) (1, 1)
Answer:
(c) (0, 1)
Hint:
y = e^x
Put x = 0, we get y = e⁰ = 1.
∴ The graph intersects the y-axis at (0, 1)

Question 8.
The minimum value of the function f(x) = |x| is:
(a) 0
(b) -1
(c) +1
(d) ∞
Answer:
(a) 0
Hint:

f(x) = |x|
f(0) = |0| = 0

Question 9.
Which one of the following functions has the property f(x) 

Answer:

Question 10.
If f(x) = 2^x and g(x)  then (fg)(x) is:
(a) 1
(b) 0
(c) 4^x

Answer:
(a) 1
Hint:
(fg) x = f(x) g(x) 

Question 11.
Which of the following function is neither even nor odd?
(a) f(x) = x³ + 5
(b) f(x) = x⁵
(c) f(x) = x¹⁰
(d) f(x) = x²
Answer:
(a) f(x) = x³ + 5
Hint:
Since it has a constant term 5.
f(x) = x³ + 5
f(-x) = (-x)³ + 5 = -x³ + 5.
It is not either f(x) or -f(x).

Question 12.
f(x) = -5, for all x ∈ R is a:
(a) an identity function
(b) modulus function
(c) exponential function
(d) constant function
Answer:
(d) constant function

Question 13.
The range of f(x) = |x|, for all x ∈ R is:
(a) (0, ∞)
(b) [0, ∞)
(c) (-∞, ∞)
(d) [1, ∞)
Answer:
(b) [0, ∞)
Hint:
[0, ∞) since in this interval 0 is included and f(0) = 0.

Question 14.
The graph of f(x) = e^x is identical to that of:
(a) f(x) = a^x, a > 1
(b) f(x) = a^x, a < 1
(c) f(x) = a^x, 0 < a < 1
(d) y = ax + b, a ≠ 0
Answer:
(a) f(x) = a^x, a > 1

Question 15.
If f(x) = x² and g(x) = 2x + 1 then (fg)(0) is:
(a) 0
(b) 2
(c) 1
(d) 4
Answer:
(a) 0
Hint:
(fg)(0) = f(o) g(o)
= 0² (2(0) + 1)
= 0(1)
= 0

Question 16.

(a) 1
(b) ∞
(c) -∞
(d) θ
Answer:
(a) 1 (By formula)

Question 17.

(a) e
(b) nx^n-1
(c) 1
(d) 0
Answer:
(c) 1 (By formula)

Question 18.
For what value of x, f(x) 

 is not continuous?
(a) -2
(b) 1
(c) 2
(d) -1
Answer:
(b) 1
Hint:
When x = 1,

 
 is not defined.

Question 19.
A function f(x) is continuous at x = a   is equal to:

(a) f(-a)

(c) 2f(a)
(d) f(a)

Question 20.

 
 is equal to:

Answer:

Question 21.

  (5e^x – 2 log x) is equal to:

Answer:

Hint:

Question 22.
If y = x and z 

(a) x²
(b) 1
(c) -x²

Answer:
(c) -x²
Hint:

Question 23.
If y = e^2x then 

(a) 4
(b) 9
(c) 2
(d) 0
Answer:
(a) 4
Hint:

Question 24.
If y = log x then y₂ =

Question 25.

(b) a^a
(c) x log_ea
(d) a^x log_ea
Answer:
(d) a^x log_ea (by formula)