I am supposed to find f(g(x)). F(x)=5x^2minus 2x=3 and g(x)=4x^2 plus 7x-5 The answer I got was 5(4x^2+7x-5)^2+-2x+3. Is this correct? Thanks!!!
To find f(g(x)), we need to substitute the expression for g(x) into f(x). Let's start by substituting g(x) into f(x):
f(g(x)) = 5(g(x))^2 - 2(g(x)) + 3
Now let's substitute the expression for g(x) into f(g(x)):
f(g(x)) = 5(4x^2 + 7x - 5)^2 - 2(4x^2 + 7x - 5) + 3
To simplify this expression, we need to expand the squared term and then distribute the coefficients:
f(g(x)) = 5(16x^4 + 56x^3 - 40x^2 + 56x^2 + 196x - 140) - 8x^2 - 14x + 10 + 3
Simplifying further:
f(g(x)) = 80x^4 + 280x^3 - 200x^2 + 280x^2 + 980x - 700 - 8x^2 - 14x + 10 + 3
Combining like terms:
f(g(x)) = 80x^4 + 280x^3 + 80x^2 + 966x - 687
So the correct answer to f(g(x)) is 80x^4 + 280x^3 + 80x^2 + 966x - 687.