Let us solve a few practice problems of Functions to understand the concept of Functions in math better.
Directions for questions 1 to 5: Read the instructions and solve the questions accordingly
f(x, y) = x2 – 2y
g(x, y) = x + y3
h(x, y) = x2 + y – 2xy
k(x, y) = x + y
Q.1.Find f(2,3) – h(1, 5)
Sol : Option B
Explanation:: f(2,3) = 22 – 2(3) = 4 – 6 = -2 h(1,5) = 12 + 5 – 2(1)(5) = -4 Now, f(2,3) – h(1, 5) = -2 – (-4) = -2 + 6 = 4
Q.2. Find h(3, 4) – g(5,2) + k(13, 4)
a) -7
b) -11
c) -13
d) -17
Sol : Option A
Explanation: h(3,4) = 32 + 4 – 2(3)(4) = 9 + 4 – 24 = -11 g(5,2) = 5 + 23 = 5 + 8 = 13 k(13, 4) = 13 + 4 = 17 Now, h(3, 4) – g(5,2) + k(13, 4) = -11 – 13 + 17 = -7
Q.3. Find k[g(2,3) , k(11, 9)])
Sol : Option D
Explanation:g(2,3) = 2 + 33 = 2 + 27 = 29 k(11, 9) = 11 + 9 = 20 Now, k[g(2,3) , k(11, 9)] = k[29 + 20] = 49
Q.4.Find h(3,4) – g(2,3)
a) 58
b) 54
d) -40
d) -23
Sol : Option C
Explanation:H(3,4) = 32 + 4 – 2(3)(4) = 9 + 4 -24 = -11 G(2,3) = 2 + 33 = 2 + 27 = 29 Now, h(3,4) – g(2,3) = -11 – 29 = -40
Q.5.Find the value of h(1,3) – h (3,1)
a) -6
b) -12
c) -17
d) -3
Sol : Option A
Explanation: : H(1,3) = 12 + 3 – 2(1)(3) = 1 + 3 – 6 = -2 H(3,1) = 32 + 1 – 2(3)(1) = 10 – 6 = 4 Therefore, -2 -4 = -6
Directions for questions 6 to 10: Read the instructions and solve the questions accordingly
- x%y means x+ y
- x&y means x – y
- x$y means x2 + y2
- x@y means x2 – y2
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Q.6.Find 3%(4&5)
Sol : Option D
Explanation: : 3% (4-5) = 3% (-1) = 3+ (-1) = 2
Q7.Find 2$(4@2)
a) 132
b) 148
c) 149
d) 134
Sol : Option B
Explanation:2$ (42 – 22) = 2$ (16-4) = 2$ 12 = 22 + 122 = 4 + 144 = 148
Q8.Find the value of (9@3) % (3&9)
Sol : Option C
Explanation: (92 – 32) % (3-9) = (81-3) % (-6) 78%(-6) = 78 + (-6) = 72
Q9.Find the value of (2&5) % (3@7)
a) -45
b) -35
c) -43
d) -38
Sol : Option C
(2-5) % (32 – 72) = (-3) % (-40) = -3-40 = -43
Q10.. Find the value of (4&3) + (3@2)
Sol : Option A
Explanation:(4-3) +(32 – 22) = 1 + 5 = 6