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- anonymous

Given f(x) = x-1/ 2, solve for f−1(5).

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- anonymous

Given f(x) = x-1/ 2, solve for f−1(5).

- katieb

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- anonymous

- anonymous

|dw:1437501005469:dw|

- freckles

replace f(x) with 5 and solve for x

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- anonymous

so i got 11?

- anonymous

i mean 2

- freckles

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

- anonymous

so -10?

- freckles

so adding 1 on both sides does not give -10

- anonymous

11=x

- freckles

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

- anonymous

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

- freckles

why did you replace x with 5?

- 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
\[f^{-1}(5)=11 \]

- anonymous

Ohh! Okay :)

- anonymous

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

- anonymous

i got 2+8i

- mathstudent55

correct

- freckles

sounds fine

- 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!

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