Question

Suppose that the functions g and h are defined for all real numbers x as follows.g(x) = 4xh(x)=2x-4Write the expressions for (hg)(x) and (h-g)(x) and evaluate (h+g)(3).

Answer 1

GIven:

The functions are

g(x) = 4x

h(x) = 2x-4.

The objective is to find the product (h*g)(x), subtraction (h-g)(x) and addition (h+g)(3) of the functions.

The value of product of the functions (h*g)(x) can be calculated as,

`\begin{gathered} (h\cdot g)(x)=(2x-4)(4x) \\ =2x(4x)-4(4x) \\ =8x^2-16x \end{gathered}`

Now, the value of subtraction of the functions (h-g)(x) can be calculated as,

`\begin{gathered} (h-g)(x)=(2x-4-4x) \\ =-2x-4 \end{gathered}`

Then, the value of addition of the functions (h+g)(3) can be calculated as,

`\begin{gathered} (h+g)(3)=(2x-4+4x) \\ =6x-4 \\ =6(3)-4 \\ =18-4 \\ =14 \end{gathered}`

Hence, the results are,

(h*g)(x) = 8x²-16x

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

(h+g)(3) = 14