Let us solve a few practice problems of Functions to understand the concept of Functions in math better.
Q.1. If f(x) = 3x + 2 & g(x) = x
2 – 1. Find f(g(-3))
Answer & Explanation
Sol : Option A Explanation: f(g(-3)) = f((-3)2 -1) = f(8) = 3(8) + 2 = 26
Q.2. Given f(x) = x
2 + x ; if x is a prime number.f(x) = 2x + 5 ; if x is non- prime
Find f(f(1))
Answer & Explanation
Sol : Option C Explanation: Now, 1 is neither prime nor composite So f(2(1) + 5) = f(7) = 72 + 7 = 56
Q.3. Given f(x) = x3 + 1,
g(x) = 2x – 5
h(x) = [f(x)]2 – g(x)
Find h(-2)
a) 34
b) -23
c) -12
d) 58
Answer & Explanation
Sol : Option D Explanation: h(-2) = [f(-2)]2 – g(-2) = [(-2)3 + 1]2 – [2(-2) -5] [-8 + 1]2 – [-4-5] = [-7]2 – [-9] = 49 + 9 = 58
Q.4. Given g(x) = x3 – x2 + 2 ; if x is an odd number
g(x) = 2x + 5 ; if x is an even number
Find g(g(3))
Answer & Explanation
Sol : Option DExplanation: Now, 3 is an odd number So, g(33 – 32 + 2) = g(27 – 9 + 2) = g(20) = 2(20) + 5 = 45
Q.5. f(x,y) = x + y ; if both x & y are even
f(x,y) = x – y ; if both x & y are odd
f(x, y) = 2x – y
2 , if any one of them is odd & other is even.
Find f(2, 3) – f(2, 4)
a) -31
b) -56
c) -11
d) -13
Answer & Explanation
Sol : Option CExplanation: f(2, 3) = 2(2) – 32 = 4 – 9 = -5 f(2, 4) = 2 + 4 = 6 Now, f(2, 3) – f(2, 4) = -5 – 6 = -11
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Q.6. f(x,y) = x
2 + y ; if both x & y are prime
f(x,y) = x + 2y ; if both x & y are composite
f(x, y) = x + y , if any one of them is prime & other is composite.
Find f(5, 3) + f(3, 6)
Answer & Explanation
Sol : Option BExplanation: f(5, 3) = 52 + 3 = 25 + 3 = 28 F(3, 6) = 3 + 6 = 9 Now, f(5, 3) + f(3, 6) = 28 + 9 = 37
Directions for questions 7 to 10: Read the instructions and solve the questions accordingly
x # y = x + y2 – y2 2
Q.7. Find 3 # (4 $ 6)
a) 23
b) 256
c) 103
d) 109
Answer & Explanation
Sol : Option CExplanation: 3 # (4+6)2 = 3 # 100 = 3 + 100 = 103
Q8. Find [3 @ (7 # ( 5 & 3) ]
a) -20
b) -23
c) -34
d) -45
Answer & Explanation
Sol : Option AExplanation: [ 3 @ (7 # (52 – 32 )] = [ 3 @ (7 # 16)] [3 @ (7 + 16)] = [ 3 @ 23] = [ 3 – 23] = -20
Q9. Find -3 $ (6 & (4 # 3))
a) 361
b) 121
c) 144
d) 987
Answer & Explanation
Sol : Option AExplanation: -3 $ (6 & (4 + 3)) = -3 $ (6 & 7) -3 $ (62 – 72 ) = -3 $ (36 – 49) = -3 $ -13 = (-3-16)2 = (-19)2 = 361
Q10. . Find the 3 $ (4 & (5 & 6))
a) -102
b) -56
c) -34
d) -23
Answer & Explanation
Sol : Option AExplanation: 3 $ (4 & (52 – 62 )) = 3 $ (4 & (25 – 36)) 3 $ (4 & -11) = 3 $ (16 -121) = 3 $ -105 = 3 -105 = -102