Question

Answer this functions question

Answer 1

`\boxed{a = 4}`

Explanation:

Note:

We have the following functions

`f(x) = (2)/(x)\\\\g(x) = (x + 1)/(x)\\`

`gf(x) = g(f(x))`

`\textrm{To find g(f(x)) wherever you see an x in gx), substitute the expression for f(x)}\\`

`Since f(x) = (2)/(x)\\\\\textrm and}\\\\g(x) = (x + 1)/(x)\\`

`\frac{\frac{{2}}{x}+1}{(2)/(x)}\\\\\\\\\left(\frac{{2}}{x}+1}\right) / (2)/(x)\\\\= \left(\frac{{2}}{x}+1} \right) * (x)/(2)\\\\`

`(2)/(x) + 1} = (2 + x)/(x)\\`

`\left(\frac{{2}}{x}+1} \right) * (x)/(2)\\\\\\= (2 + x)/(x) * (x)/(2)\\\\\\`

`\textrm{The x's cancel out giving $(2+x)/(2)$}= 1 + (x)/(2)`

`\textrm{For a specific value, a, if $g(f(a)) = 1 + (a)/(2)$ = 3}}`

`\textrm{Then $(a)/(2)$ = 3-1 = 2}`

`\boxed{a = 4}`