For the functions below, solve for f(g(h(-1))).
f(x)=(x-1)^2
g(x)=2x^2+3x-1
h(x)=(x+3)
h(-1) = 2
g(2) = 13
f(13) = 144
or
f(g(h)) = (g(h)-1)^2
= ((2h^2+3h-1)-1)^2
= (2h^2+3h-2)^2
= (2(x+3)^2+3(x+3)-2)^2
= 4x^4+60x^3+325x^2+750x+625
= 4-60+325-750+625
= 144
I think the first way is easier!
I don't get how you got that answer.
how did f(x)=(x-1)^2 become f(13) = 144
and the second way I don't get where that answer came from? can you please explain.
f(x) = (x-1)^2
so
f(13) = (13-1)^2 = 12^2 = 144
To solve for f(g(h(-1))), we will substitute the value of -1 into the function h(x) first, then substitute the result into g(x), and finally substitute the result into f(x).
Let's start by finding h(-1):
h(x) = (x + 3)
Replace x with -1:
h(-1) = (-1 + 3)
h(-1) = 2
Next, we will find g(h(-1)):
g(x) = 2x^2 + 3x - 1
Replace x with the result of h(-1):
g(h(-1)) = 2(2)^2 + 3(2) - 1
g(h(-1)) = 2(4) + 6 - 1
g(h(-1)) = 8 + 6 - 1
g(h(-1)) = 13
Now we will find f(g(h(-1))):
f(x) = (x - 1)^2
Replace x with the result of g(h(-1)):
f(g(h(-1))) = (13 - 1)^2
f(g(h(-1))) = (12)^2
f(g(h(-1))) = 144
Therefore, the value of f(g(h(-1))) is 144.