Question 197694
Is the function {{{h(t)=t-8/t}}} ???


a)

 
{{{h(t)=t-8/t}}} Start with the given function.



{{{h(x)=x-8/x}}} Plug in {{{t=x}}}



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b)

 
{{{h(t)=t-8/t}}} Start with the given function.



{{{h(1/x)=1/x-8/(1/x)}}} Plug in {{{t=1/x}}}



{{{h(1/x)=1/x-8*(x/1)}}} Flip the second fraction and multiply



{{{h(1/x)=1/x-8x}}} Multiply



{{{h(1/x)=(1-8x^2)/x}}} Combine like terms.





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OR....



Is the function {{{h(t)=(t-8)/t}}} ???


a)

 
{{{h(t)=(t-8)/t}}} Start with the given function.



{{{h(x)=(x-8)/x}}} Plug in {{{t=x}}}



---------------


b)

 
{{{h(t)=(t-8)/t}}} Start with the given function.



{{{h(1/x)=(1/x-8)/(1/x)}}} Plug in {{{t=1/x}}}



{{{h(1/x)=(cross(x)(1/cross(x))-8x)/(cross(x)(1/cross(x)))}}} Multiply EVERY term by the inner LCD "x" to clear out the inner fractions.



{{{h(1/x)=(1-8x)/1}}} Multiply and simplify



{{{h(1/x)=1-8x}}} Reduce.