Question

Suppose that the functions g and h are defined for all real numbers x as follows. g(x)=x+2 h(x) = 4x + 4 Write the expressions for (g.h)(x) and (g-h)(x) and evaluate (g+h)(1).

Answer 1

(g.h)(x) = g(x). h(x)

= (x +2)(4x + 4)

Open the parentheses

=x(4x+4) + 2(4x+4)

= 4x² + 4x + 8x + 8

= 4x² + 12x + 8

(g - h)(x) = g(x) - h(x)

=x+ 2 - (4x + 4)

= x + 2 - 4x - 4

= x - 4x + 2 - 4

= -3x - 2

To find (g+h)(1), we will first find (g+h)(x)

(g+h)(x) = g(x) + h(x)

=x + 2 + 4x + 4

=x + 4x + 2 + 4

= 5x + 6

To get, (g+h)(1), just substitute x=1 in the above

That is;

(g+h) (1) = 5(1) + 6 = 11