Therefore in each composite function we get different domains and ranges which is given below.
- Function is whose values are found from 2 given operates by applying one operate to AN variable so applying the second operate to the result and whose domain consists of these values of the variable that the result yielded by the primary function lies within the domain of the second
- The domain of a operate is that the set of values that we tend to ar allowed to plug into our operate.
- This set is that the x values in a very operate like f(x).
- The vary of a operate is that the set of values that the operate assumes. This set is that the values that the operate shoots out when we tend to plug AN x price in. they're the y values out after we plug an x value in. They are the y values.
(1) f(x) = x+2 , g(x) = 3x - 1
(f + g)(x) = f(x) + g(x)
= x+2 + 3x - 1
= 4x +1
Domain = (-∞ , ∞) and range = (-∞ , ∞)
(f - g )(x) = f(x) - g(x)
= x+2 -3x +1
= -2x + 3
Domain = (-∞ , ∞) and range = (-∞ , ∞)
(f.g)(x) = f (x) g(x)
= (x+2)( 3x - 1)
= 3x²- x + 6x - 2
= 3x²+ 5x -2
Domain = (-∞ , ∞) and range = [-49/12 ,∞)
(f/g)(x) = f(x)/g(x)
= x+2/3x-1
Domain = (-∞ , 1/3) ∪ (1/3 ,∞) and range = (-∞ , 1/3) ∪ (1/3 ,∞)
(2) f(x) = x² - 5 and g(x) = -x +8
(f + g)(x) = f(x) + g(x)
= x² - 5 -x +8
= x² - x +3
Domain = (-∞ , ∞) and range = [11/4 ,∞)
(f - g )(x) = f(x) - g(x)
= x² - 5 +x -8
= x² + x - 13
Domain = (-∞ , ∞) and range = [-53/4 ,∞)
(f.g)(x) = f (x) g(x)
= ( x² - 5 )(- x +8)
= -x³ + 8x² + 5x - 40
Domain = (-∞ , ∞) and range = (-∞ , ∞)
(f/g)(x) = f(x) / g(x)
= x² - 5 / -x +8
Domain = (-∞ , 8) ∪ (8 ,∞) and range = (-∞ , -16 - 2√59 ) ∪ (-16 + 2√59 ,∞)
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