## anonymous one year ago Given f(x) = x-1/ 2, solve for f−1(5).

1. anonymous

@Nnesha @mathstudent55

2. anonymous

|dw:1437501005469:dw|

3. freckles

replace f(x) with 5 and solve for x

4. anonymous

so i got 11?

5. anonymous

i mean 2

6. freckles

$f^{-1}(5)=x \text{ \implies} f(x)=5$ $5=\frac{x-1}{2} \\ \text{ multiply 2 on both sides } \\ 10=x-1$

7. anonymous

so -10?

8. freckles

so adding 1 on both sides does not give -10

9. anonymous

11=x

10. freckles

10=x-1 add 1 to both sides yes 10+1=x 11=x this means since $f(11)=5 \text{ then } f^{-1}(5)=11$

11. anonymous

I thought it would be 2 because 5-1/2 =2

12. freckles

why did you replace x with 5?

13. freckles

you were suppose to replace f(x) with 5 the question ask to find f inverse of 5 not f of 5 like this is the way I like to to think of it if it asked to find something like $f^{-1}(5) \\ \text{ then I call this something like } x \\ f^{-1}(5)=x \\ \text{ but if } f^{-1}(5)=x \text{ then } f(x)=5 \\ \text{ so this means I can find the } x \text{ for when } f(x) \text{ is } 5 \\ \text{ by replace } f(x) \text{ with 5 and solving for } x$ $f(x)=\frac{x-1}{2} \\ \text{ we are going \to replace } f(x) \text{ with 5, not } x \\ \text{ since we have }f(x)=5 \\5=\frac{x-1}{2} \\ \text{ now we can figure out the } x \text{ such that we do have } f(x)=5$ We figured out that that x was 11 so we have f(11)=5 so that means $f^{-1}(5)=11$

14. anonymous

Ohh! Okay :)

15. anonymous

Which of the following is the conjugate of a complex number with 2 as the real part and −8 as the imaginary part?

16. anonymous

i got 2+8i

17. mathstudent55

correct

18. freckles

sounds fine

19. mathstudent55

complex number: a + bi conjugate: a - bi As you can see , only the sign of the imaginary part changes to form the conjugate, which is what you did. Good job!