Question

If f(x) = 13 when f(x)=5x -√8, find x.

Answer 1

Given that we have the function f(x) = 5x-√8, it is equal to 13 at some value of x. This relation can be written in equation as

`5x-\sqrt[]{8}=13`

Move √8 to the other side of the equation so that only the term with x will be left on the left-hand side. We have

`5x=13+\sqrt[]{8}`

Divide both sides by 5, we get

`\begin{gathered} (5x)/(5)=\frac{13+\sqrt[]{8}}{5} \\ x=\frac{13+\sqrt[]{8}}{5} \end{gathered}`

The square root of 8 can be further simplified as

`\sqrt[]{8}=\sqrt[]{4\cdot2}=2\sqrt[]{2}`

Hence, the value of x can also be rewritten as

`x=\frac{13+2\sqrt[]{2}}{5}`

Thus, the value of x to satisfy f(x) = 13 when f(x)=5x -√8 is

`x=\frac{13+\sqrt[]{8}}{5}=\frac{13+2\sqrt[]{2}}{5}=(13)/(5)+\frac{2\sqrt[]{2}}{5}`