Functions

Example 1Given f : x ↦ h x + k , g : x ↦ ( x + 1 ) 2 + 4   and f g : x ↦ 2 ( x + 1 ) 2 + 5.   Find (a) the value of g²(2), (b) the value of h and of k. Example … Read more

Example 3 If f : x ↦ 2 x + 1   and g : x ↦ 5 x , x ≠ 0  .  Find the composite functions gf , fg and the value of gf(4).

Example 2 Functions f and g are defined by f : x ↦ x − 1   and g : x ↦ 3 − x x + 4  .  Find (a) the value of gf(3), (b) the value of fg(-1 ), (c) the composite functions fg, (d) the composite functions gf, (e) the composite functions … Read more

Example 1If f : x ↦ x + 5 ,   and g : x ↦ x 2 + 2 x + 3  , find (a) the value of gf(2), (b) the value of fg(2) (c) the composite functions fg (d) the composite functions gf (e) the composite functions g 2 (f) the composite functions … Read more

Composite Function If function f : X ↦ Y , and function g : Y ↦ Z , hence, composite function g f : X ↦ Z Example: If, f : x ↦ 2 x + 5 and g : x ↦ x 2 − 1 , find g f ( 2 ) Answer: f … Read more

Example 4Given the function f : x ↦ 3 x + 2  , find the value of (a) f ( 2 ) (b) f ( − 5 ) (c) f ( 1 3 ) Example 5If f ( x ) = x 2 + 3 x + 2  , express each of the following in … Read more

Example 2 Function f is defined as f : x → 5 2 x − 1 , x ≠ k Find the value of k. Example 3 Given g : x → 3 x − 5 2 x + 7   Function g is defined for all values of x except x = a. Find … Read more

Example 1 Given the function f : x → 6 x + 1 . Find the value of p if f ( 4 ) = 4 p + 5 .Answer: f : x → 6 x + 1 f ( x ) = 6 x + 1 f ( 4 ) = 6 ( 4 … Read more

(B) Domain, Range, Objects and Images of a Function Example: The arrow diagram above represents the function f : x → 2×2 – 5. State (a) the domain, (b) the range, (c) the image of –2, (d) the objects of (i) –3, (ii) –5.   Solution: (a) Domain = {–2, –1, 0, 1, 2}. (b) … Read more

As shown in figure above, for a function f : X → Y , each element x in the domain X has a unique image y in the codomain Y.  The function can be written as: y = f ( x ) o r f : x ↦ f ( x ) For y = … Read more