0. Functions

Introduction to Functions

0. Functions

Introduction to Functions

2:14 minutes

Problem 10Briggs - 3rd Edition

Textbook Question

Evaluating functions from graphs Assume ƒ is an odd function and that both ƒ and g are one-to-one. Use the (incomplete) graph of ƒ and g the graph of to find the following function values. <IMAGE>

ƒ(g(4))

Verified step by step guidance

Step 1: Understand the properties of the functions involved. Since

f

is an odd function, it satisfies the property

f (- x) = - f (x)

for all

x

. Both

f

and

g

are one-to-one functions, meaning they have unique outputs for each input and are invertible.

Step 2: Determine

g (4)

using the graph of

g

. Locate the point on the graph where the input is 4 and find the corresponding output value, which is

g (4)

Step 3: Use the value of

g (4)

found in Step 2 as the input for the function

f

. This means you need to evaluate

f (g (4))

by finding the output of

f

when the input is

g (4)

Step 4: Use the graph of

f

to find

f (g (4))

. Locate the point on the graph of

f

where the input is

g (4)

and determine the corresponding output value.

Step 5: Verify the result by considering the properties of odd functions and one-to-one functions. Ensure that the value found for

f (g (4))

is consistent with the properties of

f

being odd and both functions being one-to-one.

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Throwing a stone Suppose a stone is thrown vertically upward from the edge of a cliff on Earth with an initial velocity of 32 ft/s from a height of 48 ft above the ground. The height (in feet) of the stone above the ground t seconds after it is thrown is $s (t) = - 16 t^{2} + 32 t + 48$ .

d. When does the stone strike the ground?

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Velocity from position The graph of $s = f (t)$ represents the position of an object moving along a line at time $t is greater than or equal to 0$ . <IMAGE>

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