# Consider the function f(x)=(10/x^2)-(7/x^6) if f(1)=0, then what is f(x)?

Aug 21, 2015

If I'm correct that that should be $f ' \left(x\right)$ to start, then $f \left(x\right) = - \frac{10}{x} + \frac{7}{5 {x}^{5}} + \frac{43}{5}$

#### Explanation:

I'm going to guess the question is intended to be:

$f ' \left(x\right) = \left(\frac{10}{x} ^ 2\right) - \left(\frac{7}{x} ^ 6\right)$ if $f \left(1\right) = 0$, then what is $f \left(x\right)$?

$f ' \left(x\right) = 10 {x}^{-} 2 - 7 {x}^{-} 6$

$f \left(x\right) = 10 {x}^{- 2 + 1} / \left(- 2 + 1\right) - 7 {x}^{- 6 + 1} / \left(- 6 + 1\right) + C$

$= 10 {x}^{-} \frac{1}{-} 1 - 7 {x}^{-} \frac{5}{-} 5 + C$

So,

$f \left(x\right) = - \frac{10}{x} + \frac{7}{5 {x}^{5}} + C$

Now, $f \left(1\right) = - \frac{10}{1} + \frac{7}{5 \left(1\right)} + C = 0$ gets us:

$C = \frac{43}{5}$ and

$f \left(x\right) = - \frac{10}{x} + \frac{7}{5 {x}^{5}} + \frac{43}{5}$