SOLUTION: If f(x) = 2x + 3 and g(x) = (x - 3)/2, what is the value of f[g(-5)]?

If f(x) = 2x + 3 and g(x) = (x - 3)/2, 
what is the value of f[g(-5)]? 

f[g(-5)] means substitute -5 for x in the right side of g(x), 
simplify, then substitute what you get for x in the right 
side of f(x), then simplify.

It's a "double substitution".

To find f[g(-5)], work it from the inside out.

In f[g(-5)], do only the inside part first.
In this case the inside part if the red part g(-5)

g(-5) means to substitute -5 for x in 

g(x) = (x - 3)/2

So we take out the x's and we have

g(  ) = (   - 3)/2

Now we put -5's where we took out the x's, and we now 
have

g(-5) = (-5 - 3)/2

Then we simplify:

g(-5) = (-8)/2

g(-5) = -4

Now we have the g(-5)] 

f[g(-5)]  

means to substitute g(-5) for x in 

f[x] = 2x + 3

So we take out the x's and we have

f[     ] = 2[     ] + 3

Now we put g(-5)'s where we took out the x's, and we 
now have

f[g(-5)] = 2[g(-5)] + 3

But we have now found that g(-5) = -4, we can put 
that in place of the g(-5)'s and we get

f[g(-5)] = f[-4]

But then

f(-4) means to substitute -4 for x in

f(x) = 2x + 3

so 

f(-4) = 2(-4) + 3

then we simplify  

f(-4) = -8 + 3

f(-4) = -5

So

f[g(-5)] = f(-4) = -5

Edwin