Let f(x) = 3x^2 – x + 2 and g(x) = 5x^2 – 1. Find f(g(x)). Show each step of your work.

I got 75x^4 -35x +6

If that is wrong can you correct me. Thank you!

Double check your second term.

Oh...thx it is squared.

To find f(g(x)), you need to substitute g(x) into the function f(x). Let's break down the process step by step to determine if your answer is correct.

1. Start with the function f(x) = 3x^2 - x + 2.
2. Substitute g(x) into f(x), so replace every instance of x in f(x) with g(x). This gives us f(g(x)) = 3(g(x))^2 - (g(x)) + 2.
3. Replace g(x) with its expression, which is 5x^2 - 1. The function becomes f(g(x)) = 3(5x^2 - 1)^2 - (5x^2 - 1) + 2.
4. Simplify the expression within the parentheses by applying the exponent, squaring (5x^2 - 1)^2. This results in f(g(x)) = 3(25x^4 - 10x^2 + 1) - (5x^2 - 1) + 2.
5. Distribute 3 into the expression within the parentheses. You get f(g(x)) = 75x^4 - 30x^2 + 3 - 5x^2 + 1 + 2.
6. Combine like terms, which gives us f(g(x)) = 75x^4 - 35x^2 + 6.

So, your answer of f(g(x)) = 75x^4 - 35x^2 + 6 is correct. Well done!