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- Total Questions 20
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1. Find the domain of the definition of the function *y* = |*x*|.

Correct Answers :

[B]

Explanation :

*y* = |*x*| will be defined for all values of x. From = – • to + •

2. Find the domain of the definition of the function y = √*x*

Correct Answers :

[D]

Explanation :

For y = √*x* to be defined, x should be non-negative. i.e. *x* ≥ 0.

3. Find the domain of the definition of the function *y* = |√*x*|

Correct Answers :

[A]

Explanation :

Since the function contains a √x in it, x ≥ 0 would be the domain.

4. Find the domain of the definition of the function y = (x – 2)^{1/2} + (8 – x)^{1/2}.

Correct Answers :

[C]

Explanation :

For (x – 2)^{1/2} to be defined x ≥ 2.

For (8 – x)^{1/2} to be defined x £ 8.

Thus, 2 £ x £ 8 would be the required domain.

5. Find the domain of the definition of the function y = (9 – x2)^{1/2}.

Correct Answers :

[A]

Explanation :

(9 – x^{2}) ≥ 0 fi –3 £ x £ 3.

6. Find the domain of the definition of the function y = 1/(x^{2} – 4x + 3).

Correct Answers :

[D]

Explanation :

The function would be defined for all values of x except where the denominator viz: x^{2} – 4x + 3
becomes equal to zero.

The roots of x^{2} – 4x + 3x = 0 being 1, 3, it follows that the domain of definition of the function
would be all values of x except x = 1 and x = 3.

7. The values of *x* for which the functions f(*x*) = *x* and g(*x*) = (√*x*)^{2}are identical is

Correct Answers :

[B]

Explanation :

f(x) = x and g(x) = (√x )^{2} would be identical if √x is defined.

Hence, x ≥ 0 would be the answer.

8. The values of *x* for which the functions f(*x*) = *x* and g(*x*) = *x*^{2}/*x* are identical is

Correct Answers :

[A]

Explanation :

f(x) = x is defined for all values of x.

g(x) = x^{2}/x also returns the same values as f(x) except at x = 0 where it is not defined.
Hence. option (a).

9. If f(*x*) = √*x*^{3} , then f(3*x*) will be equal to

Correct Answers :

[C]

Explanation :

f(x) = √*x*^{3} fi f(3x) =√(3*x ^{3}*) = 3√(3

10. If f(x) = e^{x}, then the value of 7 f(x) will be equal to

Correct Answers :

[B]

Explanation :

7 f(x) = 7 e^{x}.

11. If f(x) = log x^{2} and g(x) = 2 log x, then f(x) and g(x) are identical for

Correct Answers :

[D]

Explanation :

While log x^{2} is defined for – • < x < • , 2 log x is only defined for 0 < x < •. Thus, the two functions are identical for 0 < x < •.

12. If f(x) is an even function, then the graph y = f(x) will be symmetrical about

Correct Answers :

[B]

Explanation :

y – axis by definition.

13. If f(x) is an odd function, then the graph y = f(x) will be symmetrical about

Correct Answers :

[D]

Explanation :

Origin by definition.

14. Which of the following is an even function?

Correct Answers :

[A]

Explanation :

x^{–8} is even since f(x) = f(–x) in this case.

15. Which of the following is not an odd function ?

Correct Answers :

[A]

Explanation :

(x + 1)^{3} is not odd as f(x) π –f(–x).

16. For what value of x, x^{2} + 10x + 11 will give the minimum value?

Correct Answers :

[C]

Explanation :

dy/dx = 2x + 10 = 0 fi x = –5.

17. In the above question, what will be the minimum value of the function?

Correct Answers :

[A]

Explanation :

Required value = (–5)^{2} + 10(–5) + 11
= 25 – 50 + 11 = –14.

18. Find the maximum value of the function 1/(x^{2} – 3x + 2).

Correct Answers :

[D]

Explanation :

Since the denominator x^{2} – 3x + 2 has real roots, the maximum value would be infinity.

19. Find the minimum value of the function f(x) = log2 (x^{2} – 2x + 5).

Correct Answers :

[B]

Explanation :

The minimum value of the function would occur at the minimum value of
(x^{2} – 2x + 5) as this quadratic function has imaginary roots.

For y = x^{2} – 2x + 5

dy/dx = 2x – 2 = 0 fi x = 1

fi x^{2} – 2x + 5 = 4.

Thus, minimum value of the argument of the log is 4.

So minimum value of the function is log2 4 = 2.

20. f(x) is any function and f ^{–1}(x) is known as inverse of f(x), then f ^{–1}(x) of f(x) = 1/x + 1 is

Correct Answers :

[C]

Explanation :

y = 1/x + 1

Hence, y – 1 = 1/x

fi x = 1/(y – 1)

Thus f^{–1}(x) = 1/(x – 1).

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