QuestionAre the functions $f(x)=21x-14$ and $g(x)=\frac{x}{21}+14$ inverses? Yes or No?

Studdy Solution

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

STEP 7

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.

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