If f(x) = 3x + 1 and g(x) = x^2 + 2x, find x when f(g(x)) = 10
Evaluate f(g(x))
f(g(x)) = 3(x^2 + 2x) + 1
f(g(x)) = 3x^2 + 6x + 1
When f(g(x)) = 10, we have
10 = 3x^2 + 6x + 1
Subtract 10 from each side:
3x^2 + 6x - 9 = 0
Divide each side of the equation by 3
x^2 + 2x - 3 = 0
Factor, we have: (x + 3)(x - 1) = 0
So x is either 1 or -3
Evaluate f(g(x))
f(g(x)) = 3(x^2 + 2x) + 1
f(g(x)) = 3x^2 + 6x + 1
When f(g(x)) = 10, we have
10 = 3x^2 + 6x + 1
Subtract 10 from each side:
3x^2 + 6x - 9 = 0
Divide each side of the equation by 3
x^2 + 2x - 3 = 0
Factor, we have: (x + 3)(x - 1) = 0
So x is either 1 or -3