1. anonymous

2. anonymous

@dan815 any help?

3. iGreen

$$\sf f(\dfrac{1}{2})$$ means to plug in 1/2 for 'x'

4. iGreen

$$\sf f(x) = 3^x$$ $$\sf f(\dfrac{1}{2}) = 3^{\frac{1}{2}}$$

5. iGreen

Simplify the right side.

6. anonymous

1.5, right?

7. iGreen

No..1/2 is an exponent, it's not being multiplied. $$\sf 3^{\frac{1}{2}} \rightarrow 3^{0.5}$$

8. iGreen

9. anonymous

I do not have one, but would it be 1/3 of 3^0.5?

10. iGreen

Well, you can't really do this without a calculator.

11. iGreen

$$\sf a^{\frac{n}{m}} \rightarrow \sqrt[m]{a^n}$$

12. iGreen

So basically we're looking at: $$\sf \sqrt[2]{3^1} \rightarrow \sqrt{3}$$

13. iGreen

$$\sf \sqrt{3} \approx 1.73205081.~.~.$$

14. iGreen

Now can you do the same with $$\sf f(\dfrac{1}{4})$$?

15. anonymous

I can try.

16. anonymous

I got 1.31607401 from the calculator I just got.

17. iGreen

Yep! $$\sf f(\dfrac{1}{4}) \rightarrow f(\dfrac{1}{4}) = 3^{\frac{1}{4}} \rightarrow \sqrt[4]{3^1} \rightarrow \sqrt[4]{3} \rightarrow 1.31607401.~.~.$$

18. iGreen

Don't forget to round both of them to the nearest hundredth.