Now let us solve a few examples of functions to understand functions in maths.
Q1. Function f is defined by f(x) = - 3 x 2 + 4 x – 13.Find f(3).
Answer & Explanation: f(3) = - 3 (3)2 + 4 (3) - 13 f(3) = -27 + 12 -13 f(3) = -28
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Q2. Function h is defined by h(x) = 7x3 + 5x – 2.Find h(-2)
Answer & Explanation: h(-2) = 7(-2)3 + 5(-2) – 2 h(-2) = 7(-8) -10 -2 h(-2) = -68
Q3.If h(2,3) = 17 & h(5,4) = 141.Find h(3,4)
Answer & Explanation: The function h(a,b) here represents a3 + b2 h(2,3) = 23 + 32 = 8+ 9 = 17 h(5,4) = 53 + 42 = 125 + 16 =141 Therefore, h(3,4) = 33 + 42 = 27 + 16 = 43
Q4.Defined that x # y = x3 + y2 – 3xy, then 4 # (5 # 6) = ?
Answer & Explanation: 4 # (5 # 6) = 4 # (125 + 16 – 90) = 4 # (51) 4 # 51 = 64 + 2601 – 612 = 2053
Q5.Defined that ak + 2 = 2ak + 1 + ak + ak - 1. If a0=2, a1=3, a2=4, then a5=
Answer & Explanation: ak + 2 = 2ak + 1 + ak + ak - 1 Put the value of k = 1, a1 + 2 = 2a1 + 1 + a1 + a1 - 1 Therefore, a3 = 2a2 + a1 + a0 Substituting values a3 = 2 (4) + 3 + 2 = 13 Using the same approach, a4 = 33 & a5 = 83.
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Q6.Given that, f(x) = x2 + 1 ; if x is even if(x) = 3x + 2; if x is odd. Find f(f(2))
Answer & Explanation: f(f(2)) =f (22 + 1) = f (5) Now f(5) = 3(5) + 2 = 17
Q7.Given f(x) = 2x-5, h(x) = x3 + 3, g(x) = x2 + 3. Find f(h(g(2))).
Answer & Explanation: f(h(g(2))) = f(h(22 + 3) = f(h(7)) f(73 + 3) = f(346) = 2(346) – 5 = 687
Q8.Given f(y) = y3 + 7, g(y) = 2y + 3, h(y) = y – 4. Find f(2) + g(2) – h(2)
Answer & Explanation: f(2) = 23 + 7 = 15 g(2) = 2(2) + 3 = 7 h(2) = 2 – 4 = -2 Now, f(2) + g(2) – h(2) = 15 + 7 – (-2) = 24
Q9.If k1 = 1 and kn + 1 – 3kn + 2 = 4n, for every positive integer n, Find k25.
Answer & Explanation: Now, k1 = 1, K2 – 3k1 + 2 = 4n K2 – 3(1) + 2 = 4(1) K2 = 5 By solving this equation, we get k2 = 5 Similarly, k3 = 21 & k4 = 73. Looking at these values we can generalise, that kn = 3n – 2n Therefore, k25 = 325 – 50
Q10.Function f is defined by f(x) = x2 - 3 ; if x is even. Function f is defined by f(x) = x2 + 1 ; if x is odd. Find f(f(2).
Answer & Explanation: f(f(2)) = f(22 - 3) = f (4-3) = f(1) F(1) = 12 + 1 = 1 + 1 = 2