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