if fxx3 and gx2x3 find fgx fxx23x10 gxx2 Find fgx fgx The do

if f(x)=x3 and g(x)=2x+3 find (f+g)(x)

f(x)=x2+3x10

g(x)=x2

Find (fg)(x)

(fg)(x)=    

The domain of (fg)(x) is x

f(x)=5x+40

g(x)=x22x80

Find (fg)(x)

(fg)(x)=    

The domain of (fg)(x) is x

Solution

f(x)=x3 , g(x)=2x+3

(f + g)(x) = x3 + 2x+3 = 3x

f(x) = x²+3x10 , g(x)=x2

(fg)(x) = (x²+3x10)(x -2) = (x² + 5x - 2x - 10)(x -2)

==> [x(x +5) -2(x +5) ] (x -2) ==> (x + 5)(x -2)²

(fg)(x) = (x + 5)(x -2)²

Domain of (fg)(x) ==> x belongs to (- , )

f(x)=5x+40

g(x)=x²2x80

(fg)(x) = (5x+40)(x²2x80)

==> (5x+40)(x²10x + 8x 80)

==> (5x+40)(x(x 10) + 8(x 10))

==> 5(x + 8)(x +8)(x -10) ==> 5(x -10)(x +8)²

Domain ==> x belongs to (- , )