FUNCTIONS : FUNCTIONS
Next term of the series 7, 11, 15, 19, 23 -------- : Next term of the series 7, 11, 15, 19, 23 --------
Slide 3 : Ans is 27
4 x 1 + 3, 4 x 2 + 3, 4 x 3 + 3, - - - - - - -
Thus nth term = 4n + 3
Rule f(x) = 4x + 3, x = 1, 2, 3, -- - - - - - -
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Slide 5 : Consider : f(x) = 4x + 3
f(0) = 4.0 + 3 = 3
f(1) = 4.1 + 3 = 7
f(2) = 4.2 + 3 = 11
Slide 6 : Q1. If f(x) = 3x + 7, and g(x) = x2, then fog(2) - gof(2) =
1. 9 2. – 7
3. – 9 4. – 150
Slide 7 : Answer is 4th option.
Slide 8 : Q2. Defined that z#x = z2 - x2, then if P#12 = 1012, P =
1. 1156 2. 34
3. 32 4. 46
Slide 9 : Answer is 2nd option.
Slide 10 : Q3. Defined that Pn+1 = 3Pn – 2Pn-1. If P0=2, P1= 4, then P9 =
1. 128 2.1024 3. 2048 4. 512
Slide 11 : Answer is 2nd option.
Slide 12 : Q4. If f(x) = x2 + 1 and g(x) = ax, find the value of f[g(x)]& g[f(x)].
Slide 13 : Answers area2x + 1
Slide 14 : Q5. If a0 = 9, a1 = 27 and a2 = 81, then the value of a60 will be
Slide 15 : The answer is 362
Slide 16 : Q6. A function f (x) is defined satisfying f (1) = 1, f (2x) = 2f (x), f (3x) = 3f(x)…….. f (nx) = nf (x).
Then f(1) + f(2) + f(3) + …f (n) equals
1. n 2. n/2 3. n(n+1)/2 4.n(n-1)/2
Slide 17 : Answer is 3rd option.
Slide 18 : Q7. x and y be real numbers and let ; f(x, y) = x + y , F (f (x, y)) = -f (x, y) & G ( f(x, y)) = -F ( f (x, y)). Which of the following expressions yields x2 as its result?
1. F (f (x, -x)) G (f (x, -x))
2. F (f (x, x)) G (f (x, x)) × 4
3. – F (f (x, x)) G (f (x, x)) log216
4. f (x, x) f (x, x)
Slide 19 : Answer is 3rd option.
Slide 20 : Q8.The greatest integer function f (x) = [x] = Greatest integer less than or equal to x. If
then which of the following values of k is impossible?
1. 13 2. 15
3. 16 4. 19
Slide 21 : Answer is 2nd option.
Slide 22 : Q9. For real number x, Let f(x) = 1/(1+x), if x is non negative.
= 1 + x, if x is negative and
fn(X) = f(fn–1(x)), n = 2, 3,......
What is the value of the product, f(2). f2(2). f3(2). f4(2). f5(2)?
1.1/3 2. 3
3. 1/18
4.None of these
Slide 23 : Answer is 3rd option.
Slide 24 : Q10. If f(x) is a polynomial satisfying
f(x). f(1/x) = f(x) + f(1/x)
and f(3) = 82, find f(4)
Slide 25 : Answer is 257.
Q11. Let Un = 2 Un -1+ 1 where [n = 1,2,3…..]. If U0 = 0, then U10 is equal to (CAT – 97) 1. 1023 2.20473.4095 4.8192 : Q11. Let Un = 2 Un -1+ 1 where [n = 1,2,3…..]. If U0 = 0, then U10 is equal to (CAT – 97) 1. 1023 2.20473.4095 4.8192
Slide 27 : Answer is 1023.
Slide 28 : Q12.The function f(x) = x – 2|+|2.5 – x| + |3.6 – x|, where x is real, f(x) attains a minimum at (CAT 2003).
1. x = 2.3 2. x = 2.5
3. x = 2.7 4.NOT
Slide 29 : Answer is
x = 2.5.
Slide 30 : Odd Function : A function is said to be odd, if f (x) = -f (-x). Its graph is symmetrical about the alternate quadrants e.g. y = x3.
Even Function : A function is said to be even, if f (x) = f (-x) i.e. the value of function remains same if you replace x by -x. Its graph is symmetrical about y-axis e.g. y = x2.
# A function is neither odd nor even,
if it does not satisfy any of the
above given conditions e.g. x3 + 2.
Slide 31 : Q13. Determine the nature of the following functions for odd and even.
Slide 32 : (i) Even (ii) Neither Even nor Odd
Q14. Let f(x) = max (2x + 1, 3 - 4x), where x is any real number. Then the minimum possible value of f(x) is (CAT 2006): 1. 1/3 2. ½ 3.2/3 4. 4/3 5.5/3 : Q14. Let f(x) = max (2x + 1, 3 - 4x), where x is any real number. Then the minimum possible value of f(x) is (CAT 2006): 1. 1/3 2. ½ 3.2/3 4. 4/3 5.5/3
Slide 34 : Answer is 5th option.
Slide 35 : THANK YOU