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Let #f(x) =abs(x+1)# and g(x) = 3x-2 how do you find (fog)(x)?

Answer 1

To find ( (f \circ g)(x) ), first substitute ( g(x) = 3x - 2 ) into ( f(x) = \lvert x + 1 ) wherever there is an ( x ) in ( f(x) ). Then, simplify the resulting expression.

So, ( f(g(x)) = \lvert g(x) + 1 ) becomes ( \lvert (3x - 2) + 1 ) after substituting ( g(x) ) into ( f(x) ).

Simplify this to get ( \lvert 3x - 1 ) which is the composition of ( f ) and ( g ), denoted as ( (f \circ g)(x) ).

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Answer 2

Benjamin Achtenberg

Answer: #|3x-1|#

#(fog)(x) = f(g(x))#

Which mean replace the g(x) into every "x" you see in the #f(x)# function.

#f(g(x))= f(3x-2) = |(color(red)(3x-2))+1|#

#= |3x - 1|#

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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.