SOLUTION: Given f(x) = sin x, g(x) = 1/x, and h(x) = |x| A) state the single equation that represents y = h(g(f(x))) B) describe what each composition does in the order that it is applie

Algebra ->  Functions -> SOLUTION: Given f(x) = sin x, g(x) = 1/x, and h(x) = |x| A) state the single equation that represents y = h(g(f(x))) B) describe what each composition does in the order that it is applie      Log On


   

Question 312054: Given f(x) = sin x, g(x) = 1/x, and h(x) = |x|
A) state the single equation that represents y = h(g(f(x)))
B) describe what each composition does in the order that it is applied.
C) sketch a curve on the interval -2pi<=x=<2pi with all the major features.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=sin%28x%29
g%28x%29=1%2Fx
h%28x%29=abs%28x%29
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a)f%28g%28h%28x%29%29%29=sin%28abs%281%2Fx%29%29
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b) h(x)- Take the absolute value of x.
g(h(x))-Take the absolute value of the reciprocal of x.
f(g(h(x))- Take the sine of the absolute value of the reciprocal of x.
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c) The function is undefined at x=0 since division by zero is undefined. But there is a lot of action as x approaches zero from both sides.

(-2%2Api%3Cx%3C2%2Api)
+graph%28+300%2C+300%2C+-7%2C+7%2C+-2%2C+2%2C+sin%28abs%281%2Fx%29%29%29+
.
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(-0.1%3Cx%3C0.1)
+graph%28+300%2C+300%2C+-.1%2C+.1%2C+-2%2C+2%2C+sin%28abs%281%2Fx%29%29%29+
.
.
.
(-0.01%3Cx%3C0.01)
+graph%28+300%2C+300%2C+-.01%2C+.01%2C+-2%2C+2%2C+sin%28abs%281%2Fx%29%29%29+
.
.
.
(-0.001%3Cx%3C0.001)
+graph%28+300%2C+300%2C+-.001%2C+.001%2C+-2%2C+2%2C+sin%28abs%281%2Fx%29%29%29+