The data in the adjacent table depicts the length of a person forehand and her corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length(x) as y = ax + b,  where a, b are constants.
(i) Check if this relation is a function.
(ii) Find a and b.
(iii) Find the height of a woman whose forehand length is 40 cm.
(iv) Find the length of forehand of a woman if her height is 53.3 inches.

Length ‘x’ of forehand (in cm)	Height 'y' (in inches)
35	56
45	65
50	69.5
55	74

Let f: A ⟶ B be a function defined by f(x) = \(\frac{x}{2}\)-1, where A = {2, 4 , 6, 10, 12}, B = {0, 1, 2, 4, 5, 9}, Represent f by
(i) set of ordered pairs
(ii) a table
(iii) an arrow diagram
(iv) a graph

The function ‘t’ which maps temperature in Celsius (C) into temperature in Fahrenheit (F) is defined by t(C) = F where F =  \(\frac{9}{5}\)C + 32. Find,
(i) t(0)
(ii) t(28)
(iii) t(-10)
(iv) the value of C whenn t(C) = 212
(v) the temperature when the Celsius value is equal to the Fahrenheit value.

If f(x) = 2x + 3, g(x) = 1 - 2x and h(x) = 3x. Prove that f o(g o h) = (f o g) o h.

Find x if gff(x) = fgg(x), given f(x) = 3x + 1 and g(x) = x + 3.

If f: R ⟶ R and g: R ⟶ R are defined by f(x) = x⁵ and g(x) = x⁴ then check if f, g are one-one and f o g is one -one?

Find the domain of the function f(x) = \(\sqrt { 1+\sqrt { 1-\sqrt { 1-x^{ 2 } } } } \).

If f(x) = \(\frac { x-1 }{ x+1 } \), x ≠ 1 show that f(f(x)) = -\(\frac{1}{x}\), provided x ≠ 0.

Let A ={x \(\in \) W| x < 2}, B={x \(\in \) N| 1 < x ≤ 4} and C = (3,5). Verify that
A x (B ∩ C) = (A x B) ∩ (A x C)

Find f o g and g and g o f when f(x) = 2x + 1 and g(x) = x² - 2