Question

if f(x) = 3x+2 and g(x) = x^2 +4, what is f(g(x))?

Answer 1

3(x^2+4)+2 <--- you get f(x) and just plug in the function of g(x) for every x you see in the f(x) equation
3x^2+12+2 <--- distribute the 3
3x^2+14 <--- add the whole numbers
3x^2+14=0 <--- set it equal to zero and get as an answer ...
x=squareroot -i(14/3) or x=squareroot i(14/3) <--- cant have a negative under the squareroot that's why we have an imaginary number

Hope this helps :)

Answer 2

@mevargas ATTENTION !

3x^2 +14 =0

3x^2 = -14

x^2 = - 14/3

x_1,2 = +/- isqrt(14/3) =

so what you can continue again ratzionalizing the denominator