If <em>h(x)</em> is the inverse of <em>f(x)</em>, then by definition of inverse function, we have
<em>f(h(x))</em> = <em>x</em>
By definition of <em>f(x)</em>, composing <em>f</em> with <em>h</em> gives
<em>f(h(x))</em> = 2 <em>h(x)</em> - 10
Solve for <em>h(x)</em> :
<em>x</em> = 2 <em>h(x)</em> - 10
2 <em>h(x)</em> = <em>x</em> + 10
<em>h(x)</em> = (<em>x</em> + 10)/2
<em>h(x)</em> = <em>x</em>/2 + 5
So... whichever option most closely resembles this is the correct one. It's hard to tell exactly which one that would be.