## anonymous one year ago If f(x) = x + 4 and g(x) = 2x - 3, find (g - f)(2). Write the answer as an integer.

1. Michele_Laino

by definition we can write: $\left( {g - f} \right)\left( x \right) = g\left( x \right) - f\left( x \right) = \left( {2x - 3} \right) - \left( {x + 4} \right) = ...?$

2. anonymous

okay

3. Michele_Laino

hint: $\begin{gathered} \left( {g - f} \right)\left( x \right) = g\left( x \right) - f\left( x \right) = \left( {2x - 3} \right) - \left( {x + 4} \right) = \hfill \\ \hfill \\ = 2x - 3 - x - 4 = ...? \hfill \\ \end{gathered}$

4. anonymous

I got 6

5. Michele_Laino

I got a different result

6. anonymous

I got 9

7. Michele_Laino

hint: $\begin{gathered} \left( {g - f} \right)\left( x \right) = g\left( x \right) - f\left( x \right) = \left( {2x - 3} \right) - \left( {x + 4} \right) = \hfill \\ \hfill \\ = 2x - 3 - x - 4 = x - 7 \hfill \\ \end{gathered}$

8. Michele_Laino

now, replace x with 2, please what do you get?

9. anonymous

-5

10. Michele_Laino

that's right!

11. anonymous

so would the answer be -5

12. Michele_Laino

yes!

13. anonymous

If f\left( x \right) = \frac{{2{x^2}}}{{x - 1}}, evaluate for f(-4). Write only the answer as a decimal or fraction. also got stuck on this question

14. Michele_Laino

is your function, like this: $f\left( x \right) = \frac{{2{x^2}}}{{x - 1}}$

15. anonymous

yes

16. Michele_Laino

we have to replace x with -4, so we can write: $f\left( { - 4} \right) = \frac{{2{{\left( { - 4} \right)}^2}}}{{ - 4 - 1}} = ...?$

17. anonymous

-13

18. Michele_Laino

hint: $f\left( { - 4} \right) = \frac{{2{{\left( { - 4} \right)}^2}}}{{ - 4 - 1}} = \frac{{2 \times 16}}{{ - 5}} = ...?$

19. anonymous

27

20. Michele_Laino

are you sure? what is 2*16=...?

21. anonymous

32

22. Michele_Laino

correct! so our answer is: $f\left( { - 4} \right) = \frac{{2{{\left( { - 4} \right)}^2}}}{{ - 4 - 1}} = \frac{{2 \times 16}}{{ - 5}} = \frac{{32}}{{ - 5}} = - \frac{{32}}{5}$

23. anonymous

okay