Question

Given that f(x)= k/x+1 + 6/x+2 and f(5)=8, Find the value of k.

Answer 1

Answer:
`k=(300)/(7)`

Explanation:

Since we know that f(5)=8, we can plug in x=5 and set that equal to 8 to find k.

`8=(k)/(5+1) +(6)/(5+2)` [add denominator]

`8=(k)/(6) +(6)/(7)` [get common denominator]

`8=(7k)/(42) +(36)/(42)` [add]

`8=(7k+36)/(42)` [multiply both sides by 42]

`336=7k+36` [subtract both sides by 36]

`300=7k` [divide both sides by 7]

`k=(300)/(7)`

Now, we know that
`k=(300)/(7)`.