First off, you need to find the composite of the two functions. Which the way it is written is asking you to plug the function f(x) in for "x" in the function g(x)...
so everywhere in g(x) I see an "x", I instead plug in "3x2 +2 x-10" so that would look like below:
g(f(x)) = 3(3x2 + 2x - 10) - 3
next we simplify this down by distributing and combining like terms
g(f(x)) = 9x2 + 6x - 30 - 3
g(f(x)) = 9x2 + 6x - 33
From there, since it is saying that g(f(x)) = 2, we set this equation equal to 2
2 = 9x2 + 6x - 33
From here we are looking to solve for x. We can do this by factoring or using the quadratic formula. Either way, we have to get the equation equal to zero first. We do this by subtracting 2 from both sides:
0 = 9x2 + 6x - 35
Because the numbers are so large, it is probably best to use the quadratic formula: (-b ±√b2 − 4ac) / 2a
From there we plug in our values: (-6 ± √62 − 4(9)(-35)) / 2(9)
Keep solving using order of operations:
(-6 ± √36 + 1260) / 18
(-6 ± √1296) / 18
(-6 ± 36) / 18
From there we finish our calculations, keeping in mind the ± that will give us two answers for x.
(-6 + 36) / 18 = 1.66666.... or 5/3
and, (-6 − 36) / 18 = -2.333.... or -7/3
