Question

How do i find out what numbers go into g(x). what are the steps to solve this question.

Answer 1

The values of the function g(x) = 3/x² and the graph of g(x) are as follows;

a. The completed table can be presented as follows;

`\begin{tabular} \cline{1-8}x &-5 & -2 &-1 &0&1&2&5 \\ \cline{1-8}g(x) & 0.12 & 0.75&3 & &3&0.75&0.12 \\\cline{1-8}\end{tabular}`

Please find attached the graph of g(x) created with MS Excel

b. Domain; (-∞, 0) ∪ (0, ∞)

Range; (0, ∞)

c. g(x) → ∞ as x → 0 and g(x) → 0 as x → ±∞

The steps used to evaluate the function can be presented as follows;

a. Please find attached the graph of g(x) = 3/x², created with MS Excel

The table completed can be completed by plugging in the values of x in the function g(x) as follows;

g(x) = 3/x²

x g(x)

-5 0.12

-2 0.75

-1 3

0 ∞

1 3

2 0.75

5 0.12

b. The domain of the function g(x) = 3/x² are the values of x for which the function is defined

The above table indicates that the function is defined for all values of x except x = 0, therefore, the domain is the set of all real numbers except 0. The domain is; Domain; (-∞, 0) ∪ (0, +∞)

Similarly the function has an output which is always positive except for zero. Therefore, the range is; (0, +∞)

c. The value of g(x) approaches zero as x approaches ±∞ and g(x) approaches infinity as x approaches zero