OPERATION IN FUNCTION
If the two functions: f (x) and g (x),
shall apply:
1. (f + g) (x) = f (x) + g (x)
2. (f - g) (x) = f (x) - g (x)
3. (f x g) (x) = f (x). g (x)
4. (f / g) (x) = f (x) / g (x)
5. fn (x) = [f (x)] n
Example :If f (x) = 2x - 3 and g (x) = 4 - x then specify:
a. (f + g) (x)
b. (f - g) (x)
c. (f x g) (x)
d. (f / g) (5)
e. f2 (-1)
Answer:
a. (f + g) (x) = 2x - 3 + 4 - x = x + 1
b. (f - g) (x) = 2x - 3 - (4 - x) = 3x - 7
c. (FXG) (x) = (2x - 3) x (4 - x) = -2x2 + 11x - 12
d. . (f) 2 (x) = (2x - 3) 2 = 4x2 - 12x + 9
e.(f) 2 (-1) = 25
Function Composition
(gof) (x) = g (f (x)), that is to say: f (x) goes to g (x)
Example:
If f (x) = 2x - 5, and g (x) = 3x + 1
determine:
a. (f o g) (x)
b. (g o f) (x)
c. (f o g) (4)
Answer:
a. (fog) (x) = f (g (x)) = 2 (3x + 1) - 5 = 6x - 3
b. (gof) (x) = g (f (x)) = 3 (2x - 5) + 1 = 6x - 14c. (f o g) (4) = 6. 4-3 = 21
nah, please piloted for training the following questions ...
A. Determine (f o g) (x) and (g o f) (1) if:1. f (x) = x2 - 4, g (x) = x + 32. f (x) = x2 - x - 6, g (x) = x2 + 2
B. Determine f (x - 2) if:1. f (x) = 3x + 72. f (x) = x2 + x - 12
C. Determine f (x) if:1. f (x + 3) = 6 - 5x2. f (2x - 7) = 4x - 33. f (2 - x) = x2 - 10 Determine f (x) or g (x) if known composition
Example:1. If (fog) (x) = 6x - 5 and f (x) = 2x + 1 then g (x) =?
Answer:
Method 1:
(fog) (x) and f (x) linear ie g (x) = ax + b(f o g) (x) = f (g (x))6x - 5 = 2 (ax + b) + 1 = 2ax + 2b + 1 g go to f => 2a = 6 a = 3, 2b + 1 = -5 b = -3obtained g (x) = 3x - 3, please check (fog) (x) =. , , , ?
Method 2:
which is known (f o g) (x) and f (x)(f o g) (x) = f (g (x))6x - 5 = 2 g + 1, 2g = 6x - 6 g (x) = 3x - 32. If the (fog) (x) = 6x - 5 and g (x) = 2x + 1 then f (x) =?Answer:Method 1: (fog) (x) and g (x) linear eg f (x) = ax + b(fog) (x) = f (g (x)), the 6x - 5 = a (2x + 1) + b = 2ax + a + b 2a = 6 a = 3, a + b = -5 b = -8obtained f (x) = 3x - 8, check (f o g) (x) =. , , , ?
Method 2:
which is known (f o g) (x) and g (x)eg, g (x) = 2x + 1 = a then x = (a-1) / 2f (a) = 6 (a-1) / 2 -5f (x) = 3x - 8
cobain exercise for ya !!!1. Define f (x) if:a. (f o g) (x) = 4x + 7 g (x) = 2xb. (f o g) (x) = x2 + 3x - 6 g (x) = x + 1c. (f o g) (x) = x2 + 3x - 18; g (x) = 2 / (x + 1)d. (f o g) (x - 2) = x2 + x - 12, g (x) = x + 32. Define f (x) if:a. (g o f) (x) = 4x + 7 g (x) = 2xb. (g o f) (x) = x2 + 3x - 6 g (x) = x + 1c. (g o f) (x) = x2 + 3x - 18; g (x) = 2 / (x + 1)d. (g o f) (x - 2) = x2 + x - 12, g (x) = x + 3
Inverse functionFIRST PICTURE CUYIf the function f = A → B is expressed by the ordered pair f = {(a, b) | a ∈ A and b ∈ B}then the inverse function of f is f-1 = b → A defined by f-1 = {(b, a) | b ∈ B and a ∈ A}.To determine the inverse function of a function can be performed in the following way.a. Make permisalan f (x) = y in the equation.b. The equations adjusted to f (x) = y, that is found in the functiony and state x = f (y).c. Replace y with x, so f (y) = f (x).