Question

The domain for f(x) and g(x) is the set of all real numbers.

Answer 1

Hi, here is the solution...

f(x) = 2$x^{2}$ + x - 3 and g(x) = x + 2

(f.g)(x) = f(x). g(x)

= (2$x^{2}$ + x - 3) *(x + 2)

Now use the distributive property, we get

= (2$x^{2}$ + x  - 3)x + 2(2$x^{2}$+x -3)

= 2$x^{3}$+$x^{2}$ -3x + 4$x^{2}$ + 2x - 6

Now combine the like terms.

= 2$x^{3}$ +5$x^{2}$-1x -6                             [-3x +2x = -1x = -x]

(f.g)(x) =  2$^{3}$+5$x^{2}$-x -6

That's it. Thank you :)