1. Given f(x) = 2 x+5.Find the values of
a)    f(3)     b) f(0)

  Given that f(x) = 2 x+5
                     (a)     f(3)  = 2×3+5
                                         = 6+5=11
                    (b)       f(0)  = 2×0+5
                                  = 0+5=5

2. Given f(x) = 3 x² + 2 .Find the values of
  a) f(4)      b)  f(±1)

   Given that f(x) = 3 x² +2
       (a) f(4) =3 × (4)²  + 2
                    = 3×16 + 2 = 48 + 2 = 50
    (b)      f(1)  = 3 × 1² + 2
               = 3 + 2 = 5
       f(-1) = 3 × (-1)² + 2 = 3 × 1 + 2
                                      = 5
         f(±1) = 5

3.Given f(x) = x² + 4 x+3 .Find the values of
a)  f(2)    b) f(¹/₂)

  a) Given that f(x) = x² + 4 x + 3
  f(2) = 2² + 4 × 2 + 3
         = 4 + 8 + 3 = 15
  f(¹/₂) = (¹/₂)² + 4 × ¹/₂ + 3
  = ¹/₄ + 2 + 3 = ¹/₄ + 5
      = ²¹/₄ = 5 ¹/₄ .

4. Given g(x) = x³ and h(x) = 4 x + 1 .Find the value of g(2) + h (2)

  Given that g(x) = x³
        g(2) = 2³ = 8
  and h(x) = 4 x + 1
      h(2) = 4 × 2 + 1 = 8 + 1 = 9
   g(2) + h(2) = 8 + 9 = 17

5. Given g(x) = x³ and h(x) = 4 x+1 .Find the value of 3 g (-1) -4h (-1)

   Given that g(x) = x³
      g(-1) = (-1) = -1
     3 g(-1) = 3 × -1 = -3
  and h(x) = 4 x + 1
    h (-1) = 4(-1) +1 = -4 + 1 = -3
    4 h(-1) = 4 × -3 = -12
Hence 3 g (-1) -4 h(-1) = -3-(-12) = -3 + 12 = 9

6. Given h(x) = 2 x+5 and g(x) = x² .Find the value of h(g(2)

  Given that g(x) = x²
                       g(2) = 2² = 4
               h(g(2)) = h(4)
                   = 2 × 4 + 5
                        = 8 + 5 = 13 .

7. If f(x) = 2 x for 0≤x≤8. Find their ranges .

   If x = 0 , f(x) = 2 × 0 = 0
  If x = 8 , f(x) = 2 × 8 = 16
    range = 0 ≤ f(x) ≤ 16

8. Of the following functions ,one is even and two are odd .Determine it .
  a) y = x⁷     b) y = x⁴ + 3 x²   c)  y = x(x² - 1)

  Let f(x) = x⁷
         f(-a)    = (-a)⁷ = -a⁷ = -f(a)
       f(x) is odd
  b)  Let f(x) = x⁴ + 3 x²
         f(-a) = (-a)⁴ + 3 (-a)² = a⁴ +3 a² = f(a)
    f(x) is even
  c)  Let f(x) = x(x² -1)
      f(-a) = -a((-a)²-1) = -a(a² -1)=-f(a)
    Hence f(x) is odd

9. State the value of the following:
a)  |-7|      b) |-1/200|   c) |9-4|

   a) We know that |x| = -x if x < 0    |-7| = - (-7)=7
b) Since |x| = -x ,|x|= |-¹/₂₀₀| = -(^-1/₂₀₀) = ¹/₂₀₀ .

c) |9-4| = |5|
     = 5 (Since |x| = x if x≥0)

10. Find the values of |x-x²| when x takes the values
   a)  2    b) ¹/₂

  |x-x² |   = |2-2²|
           = |2-4| = |-2|=2 

b) |x-x² | at x=¹/₂ = 1¹/₂ - (¹/₂)² |
                           = |¹/₂ - ¹/₄| = |²/₄|=|¹/₂|=¹/₂ 

11. The mathematics marks ,m and n ,of two twins never differ by more than 5 . Write this statement as an inequality using the modulus  sign

 Difference of m and n = m - n
Since they never differ by more than 5 , we can write this as |m - n| ≤ 5 .