Question

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

Answer 1

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