1. ## Function

$\displaystyle f(x)=7$

$\displaystyle 7=\frac{1}{2}|4x| -1$ or $\displaystyle -7=\frac{1}{2} |4x| -1$

2. ## Re: Function

$\displaystyle \dfrac{|4x|}{2}-1=7\Leftrightarrow |4x|=16\Leftrightarrow x=\pm 4$

3. ## Re: Function

Originally Posted by theloser

$\displaystyle f(x)=7$

$\displaystyle 7=\frac{1}{2}|4x| -1$ or $\displaystyle -7=\frac{1}{2} |4x| -1$

"The second one"? Do you mean $\displaystyle -7= \frac{1}{2}|4x|- 1$?
There is no reason why you should! The problem is to solve f(x)= 7, not f(x)= -7.
(And, in fact, since it leads to $\displaystyle \frac{1}{2}|4x|= -6$, there is no x satisfying that equation.)

4. ## Re: Function

$\displaystyle f(x)=|x+4|$
$\displaystyle f(x)=20$
$\displaystyle 20=|x+4| or -20=|x+4|$

Then how come for this one I should switch the signs?

5. ## Re: Function

If $\displaystyle |x+4|=20$ then, $\displaystyle x+4=20$ or $\displaystyle x+4=-20$.

6. ## Re: Function

In general:
If $\displaystyle x<0$ then $\displaystyle |x|=-x$
If $\displaystyle x>=0$ then $\displaystyle |x|=x$

So that means:
$\displaystyle 20=|x+4| \Leftrightarrow 20=x+4$
or
$\displaystyle 20=|x+4| \Leftrightarrow 20=-(x+4)$

...

7. ## Re: Function

Originally Posted by Siron
In general:
If $\displaystyle x<0$ then $\displaystyle |x|=-x$
If $\displaystyle x>=0$ then $\displaystyle |x|=x$

So that means:
$\displaystyle 20=|x+4| \Leftrightarrow 20=x+4$
or
$\displaystyle 20=|x+4| \Leftrightarrow 20=-(x+4)$

...
This really helped me understand this soo much! Thanks