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Help me to solve this question please?

Answer 1

I got #a = 1# and #b = 2#.

First of all, I assume we are just solving for #a# and #b#, since there is no #k# in the equation for #f(x)#.

For #f(x)# to be continuous, we need #ax +b# to have the same y-coordinate at #x = -1# as would #x^2#. Because #(-1)^2 = 1#, we can set #ax + b# to #1#.

#a(-1) + b = 1#

If we repeat the same process, we get the second equation.

#a(2) + b = 4#

If we solve by substitution, we get

#2a + 1 + a = 4#
#3a = 3#
#a = 1#

It follows that #b = 2#. The answer is therefore #a#.

We confirm graphically

As you can see, the graph is continuous on all #x#.

Hopefully 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.