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How do you find #f(g(x-3))# if #g(x) = x + 3# and #f(x) = x^2 - 2#?

Answer 1

To find (f(g(x-3))) given (g(x) = x + 3) and (f(x) = x^2 - 2), we substitute (g(x-3)) into (f(x)). First, we find (g(x-3)):

[ g(x-3) = (x-3) + 3 = x ]

Now, we substitute (x) into (f(x)):

[ f(g(x-3)) = f(x) = x^2 - 2 ]

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Answer 2

Elijah Allen

#f(g(x-3))=f(x)=x^2-2#

As #g(x)=x+3#, #g(x-3)=(x-3)+3=x#.

This means that writing #f(g(x-3))# is equivalent to writing #f(x)# which is just #x^2-2#.

Hence, #f(g(x-3))=f(x)=x^2-2#

Hope this helps :)

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Answer 3

Liam Brennan

To find ( f(g(x-3)) ), first find ( g(x-3) ), then substitute this expression into ( f(x) ).

Given: [ g(x) = x + 3 ] [ f(x) = x^2 - 2 ]

Find ( g(x-3) ): [ g(x-3) = (x-3) + 3 ] [ g(x-3) = x ]
Substitute ( g(x-3) ) into ( f(x) ): [ f(g(x-3)) = f(x) ] [ f(g(x-3)) = x^2 - 2 ]

So, ( f(g(x-3)) = x^2 - 2 ).

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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.