Question

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

Answer 1

Given:

g(x) = x - 1

h(x) = 2x + 4

Let's evaluate the functions for (g+h)(x) and (g.h)(x)

• (g+h)(x):

Here all we have to do is to add up both functions.

We have:

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

= (x - 1) + (2x + 4)

= x - 1 + 2x + 4

= x + 2x + 4 - 1

= 3x + 3

Thus,

(g + h)(x) = 3x + 3

• (g.h)(x)

This is to multiply both functions.

We have:

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

= (x - 1)(2x + 4)

`=\text{ 2x(x)-2x(1)+4(x)+4(-1)}`
`\begin{gathered} =2x^2-2x+4x-4 \\ =2x^2+2x-4 \end{gathered}`

• Evaluate (g - h)(-1):

First evaluate (g - h)(-1)

Use distributive property to distribute the -1 into g and h.

(g(-1) -h(-1))

= -g + h

Now evaluate (-g + h):

(-g + h) = -(x -1) + (2x + 4)

= -x + 1 + 2x + 4

= -x + 2x + 1 + 4

= x + 5

ANSWER:

`\begin{gathered} \mleft(g+h\mright)\mleft(x\mright)=3x+3 \\ \\ (g\cdot h)(x)=2x^2+2x-4 \\ \\ (g-h)(-1)=x+5 \end{gathered}`