f(x)=4x+6; g(x)=x/4-6 is the function inverse of eachother.

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- Aug 10th 2010, 08:22 PMsoniInverse Function
f(x)=4x+6; g(x)=x/4-6 is the function inverse of eachother.

- Aug 10th 2010, 08:49 PMeumyang
$\displaystyle \begin{aligned}

f(x) &= 4x+6 \\

g(x) &= \dfrac{x}{4} - 6

\end{aligned}$

I guess you want to know if f(x) and g(x) are inverses of each other? If

f(g(x)) = x and g(f(x)) = x then the answer is yes.

I'll setup both for you.

$\displaystyle f(g(x))= 4\left( \dfrac{x}{4} - 6 \right) + 6$

...

Will f(g(x)) = x?

And

$\displaystyle g(f(x))= \dfrac{4x + 6}{4} - 6$

...

Will g(f(x)) = x? - Aug 10th 2010, 08:51 PMmasoug
The very best way is to take one of the functions and "plug" it into the other

So in this case, $\displaystyle f(x)=4x+6$ and $\displaystyle g(x)=\frac{x}{4}-6$, $\displaystyle f(g(x))$ must equal $\displaystyle x$.

So the inverse of $\displaystyle f(x)=4x+6$ should be:

$\displaystyle g(x)=\frac{x-6}{4}$

Checking that would be:

$\displaystyle f(x)=4(\frac{x-6}{4})+6$

Cancel out the four,

$\displaystyle f(x)=x-6+6$

And simplify,

$\displaystyle f(x)=x$

and so it checks, $\displaystyle g(x)=\frac{x-6}{4}$ is the inverse function.

-Masoug - Aug 10th 2010, 09:15 PMsoni