Question

Help me to solve this question please?

Answer 1

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

Explanation:

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!