If f(X)= 3x+5 and g(X)= X-1, then g[f(-3)] = ??

Question

I'm having a little bit of trouble with understanding these kinds of problems 

Answer 1

First let's think about f(x).  We know f(x)=3x+5, and we can find f(-3) by substituting -3 for x:

f(x) = 3x + 5

f(-3) = 3(-3) + 5

f(-3) = -4

 

Now let's move on to g(x) = x - 1.  With g[f(-3)], we know that f(-3) = -4, so g[f(-3)] must be equal to g(-4).  (We just made a substitution of -4 for f(-3), since we just showed that they are equal.)

 

Now we just need to find g(-4), which is similar to finding f(-3).  Just substitute the number in for x!

 

Let me know if you'd like any clarification!

Answer 2

f(x) = 3x + 5

g(x) = x - 1

 

g[f(x)] = (3x + 5) - 1

g[f(x)] = 3x + 4

g[f(-3)] = 3(-3) + 4

g[f(-3)] = -9 + 4 

g[f(-3)] = -5