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Let #u(x)=2x-1# and #w(x)=x^2#, how do you find u(w(-4)) and w(u(-4))?

Answer 1

Serenity Jones

To find the values of ( u(w(-4)) ) and ( w(u(-4)) ), follow these steps:

First, find ( w(-4) ) by substituting ( x = -4 ) into the function ( w(x) = x^2 ).

( w(-4) = (-4)^2 = 16 )
Next, find ( u(w(-4)) ) by substituting the value of ( w(-4) ) into the function ( u(x) = 2x - 1 ).

( u(w(-4)) = u(16) = 2(16) - 1 = 31 )
Now, find ( u(-4) ) by substituting ( x = -4 ) into the function ( u(x) = 2x - 1 ).

( u(-4) = 2(-4) - 1 = -9 )
Finally, find ( w(u(-4)) ) by substituting the value of ( u(-4) ) into the function ( w(x) = x^2 ).

( w(u(-4)) = w(-9) = (-9)^2 = 81 )

Therefore, ( u(w(-4)) = 31 ) and ( w(u(-4)) = 81 ).

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Answer 2

Chloe Alexander

u(w(-4))=31 w(u(-4))=81

w(u(-4))

#u(x)=2x−1# #u(-4)=2(-4)−1# (plug in -4) #u(-4)=-8−1# (multiply) #u(-4)=-9# (add) #w(x)=x^2# #w(u(-4))=(-9)^2# (plug u(-4)=-9 into w(x)) #w(u(-4))=81# (square)

u(w(-4))

#w(x)=x^2# #w(-4)=(-4)^2# (plug in -4) #w(-4)=16# (square) #u(x)=2x−1# #u(w(-4))=2(16)−1# (plug w(-4)=16 into u(x)) #u(w(-4))=32−1# (multiply) #u(w(-4))=31# (add)

hope this helps

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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.