Let #f(x) = (1) / (1-3x) # and #g(x) = (1) / (x^2) # how do you find f(g(x)?

Answer 1

To find ( f(g(x)) ), you first need to substitute the function ( g(x) ) into the function ( f(x) ). So, ( f(g(x)) = f\left(\frac{1}{x^2}\right) ). Then, you substitute ( \frac{1}{x^2} ) into the function ( f(x) ) which gives ( f(g(x)) = \frac{1}{1-3\left(\frac{1}{x^2}\right)} ). Simplify this expression to get the final answer.

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Answer 2

Caleb Alexander

Put #g(x)# in place of #x# in the formula for #f(x)# and simplify to find:

#f(g(x)) = 1+3/(x^2-3)#

#f(g(x))#

#= 1/(1-3g(x))#

#= 1/(1-3(1/(x^2)))#

#= x^2/(x^2-3)#

#= (x^2-3+3)/(x^2-3)#

#= 1+3/(x^2-3)#

with restriction #x != 0#

The restriction is necessary because #g(x)# is undefined for #x = 0#, but #1+1/(x^2-3)# is normally defined when #x = 0#.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.