What is g(0) for this function?

To determine the value of $g(0)$ for a given function $g(x)$, we need to evaluate the function at $x = 0$. Let’s walk through the steps with a clear example.

Example Function

Suppose we have a function defined as $g(x) = 2x^2 – 3x + 5$

Step-by-Step Solution

1. Identify the Function: First, we note the given function is $g(x) = 2x^2 – 3x + 5$
2. Substitute $x$ with 0: To find $g(0)$, we substitute $x = 0$ into the function.

So, we have:

$g(0) = 2(0)^2 – 3(0) + 5$

3. Simplify the Expression: Next, we simplify the expression:

$g(0) = 2 times 0 – 3 times 0 + 5$

$g(0) = 0 – 0 + 5$

$g(0) = 5$

Therefore, $g(0)$ for the function $g(x) = 2x^2 – 3x + 5$ is 5.

General Process

The steps we followed can be applied to any function $g(x)$ to find $g(0)$:

1. Identify the function $g(x)$
2. Substitute $x$ with 0 in the function.
3. Simplify the result to find $g(0)$

Additional Example

Let’s consider another function to reinforce our understanding. Suppose $g(x) = frac{1}{x + 1}$

1. Identify the Function: The given function is $g(x) = frac{1}{x + 1}$
2. Substitute $x$ with 0: To find $g(0)$, we substitute $x = 0$ into the function.

So, we have:

$g(0) = frac{1}{0 + 1}$

3. Simplify the Expression: Next, we simplify the expression:

$g(0) = frac{1}{1}$

$g(0) = 1$

Therefore, $g(0)$ for the function $g(x) = frac{1}{x + 1}$ is 1.

Conclusion

Finding $g(0)$ for a function $g(x)$ involves substituting $x = 0$ into the function and simplifying the resulting expression. This method works universally for any function, whether it’s polynomial, rational, or another type. Understanding this fundamental concept is crucial for solving more complex problems in calculus and algebra.

Citations

1. 1. Khan Academy – Evaluating Functions
2. 2. Math is Fun – Functions
3. 3. Purplemath – Evaluating Functions