let f(x)= x^2-5x+6/x^2-x-6. Show that f(x) has a continuous extension to x=3....?

Question

so first off I thought it wasn't continuous at x=3 so the question to be doesn't even make sense, I dunno what formula to use to show that it 'has a continuous extension to x=3' and it also asks me to 'give a definition of the extended formula'???

what is an extended formula?

Answer 1

y=(x-3)(x-2)/(x-3)(x+2)

this is a graph with a hole at x=3

therefore not continuous at x=3

however the limit as x appro 3 from both -ve and +ve are the same andit is 1/5

ext for

y=(x-2)/(x+2)

Answer 2

First note that we can write as:

f(x) = (x^2 - 5x + 6)/(x^2 - x - 6) = (x-3)(x-2)/(x-3)(x+2) = (x-2)/(x+2), where x ~= 3



x = 3 is a removable discontinuity, so if you graph it, you should just see a whole in the graph @ x=3.



I'm not sure exactly what the phrase "has a continuous extension" means, but my best guess is the following:



Since x = 3 is a removable discontinuity, my guess would be that we can continuously extend f(x) to x=3 by writing it as

fc(x) = (x-2)/(x-3), where fc(x) is the continuous extension of f(x).

Answer 3

x2 - 5x + 6 The numbers including to make -5 would desire to multiply to equivalent +6. 2 negatives greater make a exceptional. checklist the factors of six, the numbers that multiply to make 6. 2 x 3 a million x 6 nicely -a million + -6 = -7 and -2 + -3 = -5 aha!! observed a winner you may now positioned those numbers in to interchange the 5 x2 - 2x - 3x + 6 Factorise in 2 areas just about, discover some thing that is going into each 0.5 of the bracket and save this on the exterior x(x - 2) - 3( x - 2) continually make helpful that the brakets are the comparable for the two halfs of the equation, you may now positioned the outsides of the brackets in one bracket. additionally and multiply the two mutually. (x - 2)(x-3) There we flow completely factorised. you may double verify this by skill of increasing the brackets. there is the better way of throwing the factors right now interior the bracket - yet this would nicely be a skill to coach you the way it extremely works to cut back errors interior the destiny. :)

Answer 4

try going to easycalculation.com or myalgebra.com both sites will give you the answers and even explain the step by step process

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