Question 202477
{{{f(x) = sin(x)}}}
{{{g(x) = 1/x}}}
{{{h(x) = abs(x)}}}
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what is {{{h(g(f(x)))?}}}
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start with the innermost function and work your way out.
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{{{f(x) = sin(x)}}}
{{{g(f(x)) = g(sin(x)) = 1/sin(x)}}}
{{{h(g(f(x))) = h(1/sin(x)) = abs(1/sin(x))}}}
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{{{f(x) = sin(x)}}}
whatever the value of x is, f(x) is taking that value and replacing it with the sin of that value.  {{{f(x) = sin(x)}}}, {{{f(30) = sin(30)}}}, etc.
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{{{g(x) = 1/x}}}
whatever the value of x is, g(x) is taking that value and replacing it with the reciprocal of that value.  {{{g(x) = 1/x}}}, {{{g(30) = 1/30}}}, {{{g(f(x)) = 1/f(x)}}}, etc.
if {{{f(x) = sin(x)}}}, then {{{g(f(x)) = 1/f(x) = 1/sin(x)}}}.
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{{{h(x) = abs(x)}}}
whatever the value of x is, h(x) is taking that value and replacing it with the absolute value of that value.  {{{h(x) = abs(x)}}}, {{{h(30) = abs(30)}}}, {{{h(g(x)) = abs(g(x))}}}, {{{h(g(f(x))) = abs(g(f(x)))}}}, etc.  if {{{f(x) = sin(x)}}}, and {{{g(f(x)) = g(sin(x)) = 1/sin(x)}}}, then {{{h(g(f(x))) = abs(g(f(x))) = abs(g(sin(x))) = abs(1/sin(x))}}}
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