## anonymous one year ago Complete the following statement.

1. anonymous

2. SolomonZelman

$$\LARGE\color{black}{ f(x) = \begin{cases} & x^2+2,{~~~~}{\large x\le1} \\ & ax,{~~~~~~~~~~}{\large x>1} \end{cases} }$$

3. SolomonZelman

So, you want that $$x^2+2$$, at $$x=1$$, will be equivalent to $$ax$$, at $$x=1$$.

4. anonymous

How would I do that

5. SolomonZelman

$$\large\color{black}{ \displaystyle (1)^2+2=a(1) }$$

6. SolomonZelman

a times 1 is just 1. and: (1)²+2=1+2=3

7. SolomonZelman

So the value of a that you want is equal to?

8. anonymous

To the value in x^2 + 2?

9. SolomonZelman

Again, you want $$ax$$ and $$x^2+2$$ to be equal at x=1, so that there is no discontinuity at x=1.

10. anonymous

a = 3?

11. SolomonZelman

$$\large x^2+2=ax$$ $$\large 1^2+2=a\cdot 1$$ $$\large {~~~~~~~}a~=~?$$

12. anonymous

1^2+2=3 3 * 1 = 3 a = 3 right? :)

13. SolomonZelman

yes a=3

14. SolomonZelman

I didn't see that reply. I glitched. Again, yes you are right, a=3.

15. anonymous

Thanks for teaching me :)

16. SolomonZelman

Not a problem