Given: F(x) = 2x + 5 and g(x) = x^2 and h(x) = -2x
H(g(f(x))) = ?
First, we find f(x) by plugging F(x) into the expression for f(x):
f(x) = 2x + 5
Next, we find g(f(x)) by plugging f(x) into the expression for g(x):
g(f(x)) = (2x + 5)^2
Expanding this expression gives:
g(f(x)) = 4x^2 + 20x + 25
Finally, we find h(g(f(x))) by plugging g(f(x)) into the expression for h(x):
h(g(f(x))) = -2(4x^2 + 20x + 25)
Simplifying this expression gives:
h(g(f(x))) = -8x^2 - 40x - 50
Therefore, H(g(f(x))) = -8x^2 - 40x - 50.
F(x) = 2x + 5
g(x) = x^2
h(x) = -2x
We need h(g(f(x)))
g( f(x) ) = (2x+5)^2
h( g(f(x))) = -2(2x+5)^2
= -2(4x^2 + 20x + 25)
= -8x^2 - 40x - 50
impressive, the bot got it right!
Thank you! I am glad I could help.
To find H(g(f(x))), we need to evaluate the expression step by step.
1. Start with f(x) = 2x + 5.
2. Substitute f(x) into g(x) = x^2, replacing x with 2x + 5: g(f(x)) = (2x + 5)^2.
3. Simplify the expression g(f(x)): g(f(x)) = (2x + 5)^2 = (2x + 5)(2x + 5) = 4x^2 + 20x + 25.
4. Finally, substitute g(f(x)) into h(x) = -2x, replacing x with 4x^2 + 20x + 25: H(g(f(x))) = h(g(f(x))) = -2(4x^2 + 20x + 25).
Now, you can simplify the expression further if necessary by distributing the -2 to each term within the parentheses.