Answer:
a) (f + g)(x) = 9x + 1
Domain: x ε R
b) (f - g)(x) = (-5x + 13)
Domain: x ε R
c) (f.g)(x) = 14x² + 37x - 42
Domain: x ε R
d) (f/g)(x) = (2x + 7)/(7x -6)
Domain: (x ε R except x = 6/7)
e) (f + g)(7) = 64
f) (f - g)(2) = 3
g) (f.g)(3) = 195
h) (f/g)(x) = 1/3
Step-by-step explanation:
f(x) = 2x + 7, g(x) = 7x - 6
a) (f + g)(x) = f(x) + g(x) = (2x + 7) + (7x - 6)
(f + g)(x) = 9x + 1
Since x is defined for functions f & g for all real numbers, the domain of (f + g)(x) is x ε R
b) (f - g)(x) = f(x) - g(x) = (2x + 7) - (7x - 6)
(f - g)(x) = (-5x + 13)
Since x is defined for functions f & g for all real numbers, the domain of (f - g)(x) is x ε R
c) (f.g)(x) = f(x) × g(x) = (2x + 7)(7x - 6)
(f.g)(x) = 14x² - 12x + 49x - 42 = 14x² + 37x - 42
Since x is defined for functions f & g for all real numbers, the domain of (f.g)(x) is x ε R
d) (f/g)(x) = f(x)/g(x) = (2x + 7)/(7x -6)
x is defined for functions f & g for all real numbers, the domain of (f/g)(x) will be x ε R except when the denominator vanishes (that is, goes to zero). This will cause the function to take up values of ∞.
This will happen when 7x - 6 = 0, x = 6/7.
Therefore, the domain of (f/g)(x) is x ε R except the point, x = 6/7.
e) (f + g)(7) = 9(7) + 1 = 64
f) (f - g)(2) = -5(2) + 13 = 3
g) (f.g)(3) = 14(3²) + 37(3) - 42 = 195
h) (f/g)(27) = (2(27) + 7)/(7(27) - 6) = 61/183 = 1/3
Hope this Helps!!!
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