Evaluate each expression using the given table of values ...

Evaluate each expression using the given table of values $$\begin{array}{|c|c|c|c|c|c|}\hline x & {-2} & {-1} & {0} & {1} & {2} \\ \hline f(x) & {1} & {0} & {-2} & {1} & {2} \\ \hline g(x) & {2} & {1} & {0} & {-1} & {0} \\ \hline\end{array}$$ a. $f(g(-1)) \quad$ b. $g(f(0)) \quad$ c. $f(f(-1))$ d. $f(f(2)) \quad$ e. $g(f(0)) \quad$ f. $f(g(1 / 2))$

Evaluate each expression using the given table of values
$$\begin{array}{|c|c|c|c|c|c|}\hline x & {-2} & {-1} & {0} & {1} & {2} \\ \hline f(x) & {1} & {0} & {-2} & {1} & {2} \\ \hline g(x) & {2} & {1} & {0} & {-1} & {0} \\ \hline\end{array}$$
a. $f(g(-1)) \quad$ b. $g(f(0)) \quad$ c. $f(f(-1))$
d. $f(f(2)) \quad$ e. $g(f(0)) \quad$ f. $f(g(1 / 2))$

Key Concepts

Domain and Range

Understanding the range of inputs (domain) and the possible outputs (range) is crucial when evaluating functions, especially when dealing with composite functions. The table provides a clear depiction of the values over which the functions are defined, which is essential for correctly interpreting the results and ensuring that the inputs used are valid.

Table Lookup for Functions

When functions are presented in a table format, the evaluation process involves matching the input value to the corresponding output in the table. This method is particularly useful in problems where functions are defined discretely rather than by an algebraic expression.

Function Evaluation

This concept involves finding the value of a function for a particular input. It requires substituting the given input into the function and reading or computing the corresponding output according to its definition, whether provided by an algebraic expression, a graph, or a table.

Composite Functions

Composite functions are formed when the output of one function becomes the input of another. Evaluating composite functions involves working from the innermost function outward, ensuring that each function is correctly applied in sequence.

Transcript

00:01 Hello, we need to find a value at six expressions, first being f of g of minus 1.

00:13 So f of g of minus 1 would be we need to take a look at the table if x is given as the possible values of x are minus 2, minus 1, 0 and 2.

00:27 We see the function values of x and g we have a look at what g of minus 1 is g of minus 1 is 1 so this is if of 1 and now we turn back to the table and see what if of is is there a missing number here yes if there is we should have f of 1 here as well and in the table f of 1 is given as 1 so f of 1 is 1 part b in part b we need to calculate or evaluate g of f of 0 okay g of 0 again we'll be using the table the first thing that we need is the first thing we need to see how much is f of zero.

01:44 So in the column zero we will find what f of zero is.

01:49 The table gives us minus two.

01:54 And then in the column of minus two we find what g.

01:59 So this is g of minus two and g of minus two in the table is two.

02:09 And that's it.

02:11 See, the expression is f of, f of minus one.

02:21 In the table, we look for how much f of minus one is.

02:31 F of minus one.

02:35 The table gives us that it's zero.

02:38 So it's f of zero.

02:41 We replace f of minus one.

02:43 With zero and then we look at what f of zero is f of zero is according to the table right on to the next one d asks us to or evaluate g of g of g of two g of g of two eyes to the table 2 and g of 2 will be this value here in the table which is 0 so this is replaced to 0 g of 0 and then we look in the table how much g of 0 is if x is 0 then g of 0 is 0 so how much that is next is there a next yes there is a b cd e of f of minus 2.

03:58 First the inner, f of minus 2...

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