Given that f(x)=8/(x-1) and g(x)=12/(x+12).

Question

Find f+g(x), f-g(x), (fg)(x), (f/g)(x).?

Answer 1

The functions are f(x) = 8/(x - 1) and g(x) = 12/(x + 12)

(f + g)(x) = f(x) + g(x)

= 8/(x - 1) + 12/(x + 12)

= [ 8(x + 12) + 12(x - 1)]/[(x - 1)(x + 12)]

= (8x + 96 + 12x - 12)/(x² + 12x - x - 12)

(f + g)(x) = (20x + 84)/(x² + 11x - 12).

 

(f - g)(x) = f(x) - g(x)

= 8/(x - 1) - 12/(x + 12)

= [ 8(x + 12) - 12(x - 1)]/[(x - 1)(x + 12)]

= (8x + 96 - 12x + 12)/(x² + 12x - x - 12)

(f - g)(x) = (- 4x + 108)/(x² + 11x - 12).

Comments

Contd...

(fg)(x) = f(x)g(x)

= [8/(x - 1)][12/(x + 12)]

= 96/[(x - 1)(x + 12)]

(fg)(x) = 96/(x² + 11x - 12).

 

(f/g)(x) = f(x)/g(x)

= [8/(x - 1)]/[12/(x + 12)]

= [8/(x - 1)][(x + 12)/12]

= 2(x + 12)/3(x - 1)

(f/g)(x) = (2x + 24)/(3x - 3).