Math Snap

STEP 1

Assumptions1. The function $f(x)$ is defined as $f(x) =21x -14$
. The function $g(x)$ is defined as $g(x) = \frac{x}{21} +14$
3. We need to check if these functions are inverses of each other

STEP 2

To check if two functions are inverses of each other, we need to verify two conditions1. $f(g(x)) = x$
2. $g(f(x)) = x$

STEP 3

First, let's calculate $f(g(x))$. We substitute $g(x)$ into the function $f(x)$.
$$f(g(x)) =21(g(x)) -14$$

STEP 4

Now, substitute the expression for $g(x)$ into the equation.
$$f(g(x)) =21\left(\frac{x}{21} +14\right) -14$$

STEP 5

implify the equation.
$$f(g(x)) = x +294 -14$$

STEP 6

implify further.
$$f(g(x)) = x +280$$

As we can see, $f(g(x))$ does not equal to $x$. Therefore, the first condition is not satisfied. Hence, the functions $f(x)$ and $g(x)$ are not inverses of each other.
The answer is No, they are not inverses.