Question

Function Evaluation, Rule of 4 On the right are four functions, each using one of the function representations we've learned about in this lesson. Use functions, $f(x)$, $g(x)$, $h(x)$ and $p(t)$ to answer the questions on the left. Evaluate $f(5)$ f(5) = $f(x)$ Determine $x$ when $f(x) = 0$ x = Evaluate $g(7)$ g(7) = Determine $x$ when $g(x) = 23$ x = Evaluate $h(-8)$ h(-8) = Determine $x$ when $h(x) = 174$ x = Evaluate $p(23)$ p(23) = Determine $t$ when $p(t) = -5$ t = g(x): \{(-17,23), (-16,67), (-12,35), (-5,-9), (7,40), (23,81), (29,15), (31,7), (44,26), (82,1)} $\begin{array}{|c|c|} \hline t & p(t) \\ \hline -17 & 70 \\ -16 & 23 \\ -12 & 87 \\ -5 & 89 \\ 7 & 35 \\ 23 & 90 \\ 29 & 48 \\ 31 & 49 \\ 44 & -5 \\ 82 & 117 \\ \hline \end{array}$ h(x) = -16x - 2

          Function Evaluation, Rule of 4
On the right are four functions, each using one of the function representations we've learned about in this lesson.
Use functions, $f(x)$, $g(x)$, $h(x)$ and $p(t)$ to answer the questions on the left.
Evaluate $f(5)$
f(5) = 
$f(x)$
Determine $x$ when $f(x) = 0$
x = 
Evaluate $g(7)$
g(7) = 
Determine $x$ when $g(x) = 23$
x = 
Evaluate $h(-8)$
h(-8) = 
Determine $x$ when $h(x) = 174$
x = 
Evaluate $p(23)$
p(23) = 
Determine $t$ when $p(t) = -5$
t = 
g(x): \{(-17,23), (-16,67), (-12,35), (-5,-9), (7,40), (23,81),
(29,15), (31,7), (44,26), (82,1)}
$\begin{array}{|c|c|}
\hline
t & p(t) \\
\hline
-17 & 70 \\
-16 & 23 \\
-12 & 87 \\
-5 & 89 \\
7 & 35 \\
23 & 90 \\
29 & 48 \\
31 & 49 \\
44 & -5 \\
82 & 117 \\
\hline
\end{array}$
h(x) = -16x - 2

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Function Evaluation, Rule of 4
On the right are four functions, each using one of the function representations we've learned about in this lesson.
Use functions, f(x), g(x), h(x) and p(t) to answer the questions on the left.
Evaluate f(5)
f(5) =
f(x)
Determine x when f(x) = 0
x =
Evaluate g(7)
g(7) =
Determine x when g(x) = 23
x =
Evaluate h(-8)
h(-8) =
Determine x when h(x) = 174
x =
Evaluate p(23)
p(23) =
Determine t when p(t) = -5
t =
g(x): {(-17,23), (-16,67), (-12,35), (-5,-9), (7,40), (23,81),
(29,15), (31,7), (44,26), (82,1)
t p(t)

-17 70

-16 23

-12 87

-5 89

7 35

23 90

29 48

31 49

44 -5

82 117
h(x) = -16x - 2

Added by John G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Kathleen Carty

01/12/2023

Step 1

Step 1: Evaluate f(5): f(5) = 3(5) - 2 = 15 - 2 = 13 Show more…

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Function Evaluation, Rule of 4 On the right are four functions, each using one of the function representations we've learned about in this lesson. Use functions, f(x), g(x), h(x), and p(t) to answer the questions on the left. Evaluate f(5) f(5) = ◻ Determine x when f(x) = 0 x = ◻ Evaluate g(7) g(7) = ◻ Determine x when g(x) = 23 x = ◻ Evaluate h(-8) h(-8) = ◻ Determine x when h(x) = 174 x = ◻ Evaluate p(23) p(23) = ◻ Determine t when p(t) = -5 t =

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00:01 Okay, so for problems like number one, we are given f of x is 4x plus 8, and g of x is 7 minus x squared.

00:15 We want to find f of g of 0, and then we want to find g of f of zero.

00:23 So you work inside out.

00:25 We first want g of 0, so that's 7 minus 0 squared, which is 7 minus 0, which is then what you're going to do is you're going to replace g of 0 with what it equals.

00:37 So now you want f of 7, which is 4 times 7 plus 8 or 28 plus 8, which is 36.

00:48 Now you want to go the other way.

00:50 So we want to start with f of 0.

00:54 That's 4 times 0 plus 8, which is 8.

00:59 Now we want g of 8, which is 7 minus 7.

01:03 8 squared or 7 minus 64, which is just going to give us negative 57.

01:13 And that's how you would do the top section.

01:17 Now in the next section, we have this table.

01:21 And for number 5, for example, we want f of g of 8.

01:25 So what that tells us is find the value of g when the input is 8.

01:32 So g of 8 is 4.

01:34 Which now means we want f of 4.

01:38 So go to 4 and now find the f value.

01:42 That's going to give you 4.

01:44 Let's try a couple more.

01:47 F of g of 5.

01:49 Start with g of 5, go to 5.

01:52 Look in the g column, that's 8...

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