Questions: You turn to the next task that you were assigned, where an object is moving at a constant speed of 3.4 meters per second (m / s). a. Find the distance d that the object as a function of the time spent moving, t. Call this function d(t). Use , an asterisk, for any multiplication and /, a slash, for any division. d(t)=3.4 t b. Find the inverse function by expressing the time spent moving, t, in terms of the distance moved, d. Call this function t(d). Use *, an asterisk, for any multiplication and /, a slash, for any division.

You turn to the next task that you were assigned, where an object is moving at a constant speed of 3.4 meters per second (m / s).
a. Find the distance d that the object as a function of the time spent moving, t. Call this function d(t). Use *, an asterisk, for any multiplication and /, a slash, for any division.
d(t)=3.4 * t
b. Find the inverse function by expressing the time spent moving, t, in terms of the distance moved, d. Call this function t(d). Use *, an asterisk, for any multiplication and /, a slash, for any division.

Transcript text: You turn to the next task that you were assigned, where an object is moving at a constant speed of 3.4 meters per second $(\mathrm{m} / \mathrm{s})$. a. Find the distance $d$ that the object as a function of the time spent moving, $t$. Call this function $d(t)$. Use *, an asterisk, for any multiplication and /, a slash, for any division. \[ d(t)=3.4 \cdot t \] b. Find the inverse function by expressing the time spent moving, $t$, in terms of the distance moved, d. Call this function $t(d)$. Use *, an asterisk, for any multiplication and $/$, a slash, for any division.

Solution

Solution Steps

Step 1: Define the Distance Function $d(t)$

The object is moving at a constant speed of $3.4 \, \text{m/s}$. The distance $d$ traveled by an object moving at a constant speed is given by the formula:

\[ d = \text{speed} \times \text{time} \]

Thus, the distance as a function of time $t$ is:

\[ d(t) = 3.4 \times t \]

Step 2: Find the Inverse Function $t(d)$

To find the inverse function, we need to express time $t$ in terms of distance $d$. Starting from the equation:

\[ d = 3.4 \times t \]

We solve for $t$ by dividing both sides by $3.4$:

\[ t = \frac{d}{3.4} \]

Thus, the inverse function $t(d)$ is:

\[ t(d) = \frac{d}{3.4} \]