A nonzero value for c such that f(c)=c

[hcinic]

Pls help! A nonzero value for c such that f(c)=c

Hi! I'm new here and am struggling with a HW problem in my Precalculus class.
The problem states to find a value for 'c' such that f(c)=c

the equation is: x^2 - 4x - c

I know the answer is c=6, but do not know how to get here algebraically. Any help would be greatly appreciated!

 

[daon2]

Hi! I'm new here and am struggling with a HW problem in my Precalculus class.
The problem states to find a value for 'c' such that f(c)=c

the equation is: x^2 - 4x - c

I know the answer is c=6, but do not know how to get here algebraically. Any help would be greatly appreciated!

\(\displaystyle f(c) = c^2-4c-c = c^2-5c\)

Set this equal to \(\displaystyle c\) and use your knowledge of solving quadratic equations to solve for the value(s) of \(\displaystyle c\).

 

[mmm4444bot]

Do you understand function notation?

The given function is f(x) = x^2 - 4x - c

They ask you to find a value for c that equals the number f(c).

The symbol f(c) is function notation for the expression c^2 - 4c - c.

In other words, f(c) is a symbol that represents x^2 - 4x - c only after we substitute x = c.

So, set the expression for f(c) equal to c, and solve that equation. :cool:

PS: In future posts, please mention what you've thought about or tried thus far. Cheers.

 

[hcinic]

\(\displaystyle f(c) = c^2-4c-c = c^2-5c\)

Set this equal to \(\displaystyle c\) and use your knowledge of solving quadratic equations to solve for the value(s) of \(\displaystyle c\).

correct me if i'm wrong but

c^2 - 5c = 0 gives me c = 0 and 5

but this can't be right

 

[mmm4444bot]

c^2 - 5c = 0

Oops -- you're not paying close-enough attention.

You wrote f(c) = 0 above!

 

[hcinic]

correct me if i'm wrong but

c^2 - 5c = 0 gives me c = 0 and 5

but this can't be right

OK, i missed that. Oops. Now I get it. Thank you!

 

[lookagain]

\(\displaystyle f(c) = c^2-4c-c = c^2-5c\)

Set this equal to \(\displaystyle c\) and use your knowledge of solving quadratic equations to solve for the value(s) of \(\displaystyle c\).

(OP, I took credit for this post as the author abdicated it.)

 

[Mrspi]

(OP, I took credit for this post as the author abdicated it.)

Oh really? Is this a sneaky way of getting more "votes?"

Not sure why that matters, but apparently it does.