1. ## Function

$f(x)=7$

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

2. ## Re: Function

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

3. ## Re: Function

Originally Posted by theloser

$f(x)=7$

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

"The second one"? Do you mean $-7= \frac{1}{2}|4x|- 1$?
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 $\frac{1}{2}|4x|= -6$, there is no x satisfying that equation.)

4. ## Re: Function

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

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

5. ## Re: Function

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

6. ## Re: Function

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

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

...

7. ## Re: Function

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

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

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