Question

Given that ( f(x) = x^2 + 2x + 3 ) and ( g(x) = 4x^3 - 3 ), solve for ( f(g(x)) ) when ( x = 2 ).

a) 2
b) 5
c) 11
d) 33

Answer 1

The value of f(g(x)) when x = 2 is 902.

Step-by-step explanation:

To find the value of f(g(x)) when x = 2, we first need to substitute the value of x into the function g(x). So, g(2) = 4(2)^3 - 3 = 4(8) - 3 = 32 - 3 = 29.

Now, we substitute the value g(2) = 29 into the function f(x). So, f(g(2)) = f(29) = 29^2 + 2(29) + 3 = 841 + 58 + 3 = 902.

Therefore, when x = 2, f(g(x)) = 902.