Question

Please help !!!
f=x/1+x^2 G=-x H=3^x
is F(H(G(x))) = 3^-x/ 1+3^2(-x) ?

Answer 1

\[ G{(x)} = -x \\ H{(x)} = 3^x \\ H{(G{(x)})} = 3^{G(x)} = 3 ^ {-x}\] \[ \\F(x) = \frac{x}{1+x^2} \\ F{(H{(G{(x)})})} = \frac{H{(G{(x)})}}{1 + (H{(G{(x)})})^2} = \frac{3^{-x}}{1 + (3^{-x})^2} = \frac{3^{-x}}{1 + 3^{-2x}} \]

which is what I think you had. So yes1 :)

Answer 2

if I wanted to break this sin^2(10^x) into three functions would it be A= Sin(x) B=Sin^2 C=10^x ?

Answer 3

Thank you btw

Answer 4

Not if you want three separate functions; in your example B = A^2

If you want it in the same form (kinda) as this problem, you'd have

\[ A(x) = x \\ B(x) = 10^x \\ C(x) = \sin x \]

Then your original function could be expressed as C(B(A(x)))

Answer 5

:)

Answer 6

(C(B(A(x))))^2

Answer 7

Thank you !! :)

Answer 8

C(x) could be sin^2 (x) , but either way, you're welcome ^^