Functions Help!

I have no idea, but try this:

2(ax+b)-5 is supposed to equal 3x+4, right? From there, it is just algebra.

(don't send hate, I'm 11)

Wait, how about if you equal 2b=4, so b=2. It will be better if you match both sides! Also, 2ax=3x, x will cancel, thus 2a=3, a=3/2. Therefore, 3/2+2=7/2.

g ( f(x) ) =   2 [ ax + b ] - 5   = 2ax + 2b - 5

So....we have

2ax + 2b -  5  = 3x + 4

This implies that

2ax = 3x  ⇒   2a = 3 ⇒  a = 3/2

And

2b - 5 = 4    add 5 to both sides

2b = 9       divide both sides by 2

b = 9/2

So

a + b   =     3/2 + 9/2    =  12 / 2    =   6

Another way to approach it is realization!

While we can solve for $a$ and $b$ individually, it is simpler to note that $f(1) = a + b$. Thus, substituting $1$ into the given equation, we obtain$g(f(1)) = 3 \cdot 1 + 4 = 7.$Thus, $g(f(1)) = 2 \cdot f(1) - 5 = 7 \Longrightarrow f(1) = \boxed{6}.$