Question 259095
<pre><font size = 4 color = "indigo"><b>
Given P(<font color = "red">x</font>)=4<font color = "red">x</font>+7, write P(<font color = "red">-2+h</font>)-P(<font color = "red">-2</font>)

Notice that the function letter P always has a parentheses 
( ) right after it.  It starts off with an x in there.

Whatever is in the parentheses ( )after the function letter P is
what you are supposed to substitute in place of the letter x

When you see the definition for P(x), namely this

P(<font color = "red">x</font>)=4<font color = "red">x</font>+7 

Since there are parenthese around the x after the P,
to see it better, put any x's which are on the right side in 
parentheses too, like this:

P(<font color = "red">x</font>)=4(<font color = "red">x</font>)+7 

Now empty the x's out those parentheses like this:

P(  )=4(  )+7

That's the way you should think of a function equation. Whatever
anybody puts in the parentheses on the left, that's what you must
put in the parentheses on the right side.

So when you see P(<font color = "red">-2+h</font>)  that means to put <font color = "red">-2+h</font> in the parentheses
on both the left and right of this

P(  )=4(  )+7

and get

P(<font color = "red">-2+h</font>)=4(<font color = "red">-2+h</font>)+7

Then you simplify the right side, (but not the left), and get

P(<font color = "red">2+h</font>)=-8+4h+7
P(<font color = "red">-2+h</font>)=-1+4h


Likewise when you see P(<font color = "red">-2</font>)  that means to put <font color = "red">-2</font> in the parentheses
on both the left and right of this

P(  )=4(  )+7

and get

P(<font color = "red">-2</font>)=4(<font color = "red">-2</font>)+7

Then you simplify the right side, but not the left, and get

P(<font color = "red">-2</font>)=-8+7
P(<font color = "red">-2</font>)=-1

Therefore when you see

P(<font color = "red">-2+h</font>)-P(<font color = "red">-2</font>)

since P(<font color = "red">-2+h</font>)=-1+4h 

and

since P(<font color = "red">-2</font>)=-1

therefore 

P(<font color = "red">-2+h</font>)-P(<font color = "red">-2</font>) 

means 

(-1+4h)-(-1)

then you simplify that:

P(<font color = "red">-2+h</font>)-P(<font color = "red">-2</font>) = (-1+4h)-(-1)

P(<font color = "red">-2+h</font>)-P(<font color = "red">-2</font>) = -1+4h+1

P(<font color = "red">-2+h</font>)-P(<font color = "red">-2</font>) = 4h

That's all there is to it.  It's so simple it's confusing!

Whatever is in the parentheses after the function letter,
that is what you are supposed to substitute for x in the
original equation for P(x).

Edwin</pre>