Let f : R → R : f(x) = 2x + 5 and g : R → R : g(x) = x2 + x.
Find
(i) (f + g) (x)
(ii) (f – g) (x)
(iii) (fg) (x)
(iv) (f/g)(x)
(i) Given:
f(x) = 2x + 5 and g(x) = x2 + x
(i) To find: (f + g) (x)
= (2x + 5) + (x2 + x)
= 2x + 5 + x2 + x
= x2 + 3x + 5
Therefore,
(f + g) (x) = x2 + 3x + 5
(ii) To find: (f - g) (x)
= (2x + 5) - (x2 + x)
= 2x + 5 - x2 - x
= -x2 + x + 5
Therefore,
(f + g) (x) = -x2 + x + 5
(iii) To find: (fg)(x)
(fg)(x) = f(x).g(x)
= (2x + 5).(x2 + x)
= 2x(x2) + 2x(x) + 5(x2) + 5x
= 2x3 + 2x2 + 5x2 + 5x
= 2x3 + 7x2 + 5x
Therefore,
(fg) (x) = 2x3 + 7x2 + 5x
(iv) To find
Therefore,
1