The function f(x) is each input value of ‘x’ gives exactly one output. It is generally denoted by f,g,and h. It is being pronounced as function f of ‘x’ or function g of ‘x’ or function h of ‘x’.
Example 1 ; f(x) = 5x – 6 , find the value of f(1) ?
Answer :
Now put some value of x = 1 ; then f(1) = 5 x 1 – 6 = -1
x =5 f(5) = 5 x 5 – 6 = 19
Domain – It is set of all permissible input of variable ‘x’ for that function.
Range – All the output value of function is known as range which is f(x) or y.
Example 2. g(x) = 2x + 3 for 0 < x < 3
Answer ; Here the domain is set of all possible real values of x .
This domain can be a variable also ;
Example 3 . h(x) = a2 + 5a, find the value of h(x-2)?
Answer – h(x-2) = (x-2)2 + 5 (x-2)
= x2 – 2x + 4 + 5x – 10
= x2 + 6x – 6
Compound Function
In the compound function, one function operated on other function written as f(h(x)) and pronounced as function f of h of x. It is solved from inside to outside means first h(x) will be solved and then the output is placed into outer function f.
Keep in mind that
f(h(x)) ≠ h (f(x))
Example 4 ; f(x) = x2 + 9 and h (x) = 3x – 1, find f(h(5))?
Answer ;
Start solving first inside to outside
h (5) = 3 x 5 – 1 = 14
f(h(5)) = f(14) = 142 + 9 = 205
Example 5 ; Find the value of h(f(6)) if f(x) = 2x + 3x2 and h(x) = 5x -6 ?
Answer ;
Start Solving from inside to outside
f(6) = 2 x 6 + 3 x 62 = 12 + 108 = 120
h(f(6)) = h(120) = 5x – 6 = 5 x 120 – 6 = 594.
