The domain for (a) , (b) , (c) is all set of real numbers , for (d) (x ε R except x = 3/8.
The complete question is
a) (f + g)(x), (b) (f – g)(x), (c) (f × g)(x), (d) (f / g)(x), (e) (f + g)(7), (f) (f - g)(2), (g) (f.g)(3), (h) (f/g)(27)
A function is the law that defines the relation between independent and a dependent variable.
It is given that
f(x) = 3x+8
g(x) = 8x-3
(a) (f + g)(x) = 3x+8 +8x-3 = 11x+5
(b) (f – g)(x) = 3x+8 -8x+3 = -5x +11
(c) (f × g)(x) = (3x+8)(8x-3) = 24x²-9x+64x -24 = 24x² +55x-24
(d)(f / g)(x) = (3x+8)/(8x-3)
(e) (f + g)(7) = 11*7+5 = 77+5 = 82
(f) (f - g)(2)= -5*2 +11 = 1
(g) (f.g)(3) =24*9 +55*3 -24 = 357
(h) (f/g)(27) = (3x+8)/(8x-3) = (3 * 27 +8)/(8*27-3) = 89/213
The domain for (a) , (b) , (c) is all set of real numbers , for (d) (x ε R except x = 3/8)
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