Given f(x)= x^2-3+2 and g(x)=2x-4 find (fg)(-3)
g(-3) = -10
f(-10) = ?
Didn't you mean f(x) = x^2 -3x + 2 ?
It looks like you made a typing error.
yes that is what I mean. sorry.
To find (fg)(-3), we need to evaluate the composite function (fg)(x) at x = -3.
First, let's find f(g(x)). Substitute g(x) into f(x), like this:
f(g(x)) = (g(x))^2 - 3(g(x)) + 2
Now, substitute g(x) = 2x - 4:
f(g(x)) = (2x - 4)^2 - 3(2x - 4) + 2
Simplifying further:
f(g(x)) = (4x^2 - 16x + 16) - (6x - 12) + 2
= 4x^2 - 16x + 16 - 6x + 12 + 2
= 4x^2 - 22x + 30
Now, evaluate f(g(x)) at x = -3:
f(g(-3)) = 4(-3)^2 - 22(-3) + 30
= 4(9) + 66 + 30
= 36 + 66 + 30
= 132 + 30
= 162
Therefore, (fg)(-3) = 162.