Answer:
Step-by-step explanation:
[tex]let~g(x)=2x+3,~ then~f\circ g(x)=f(g(x)=3x-8\\\\[/tex]
lets assume that f(x) is a line, so f(x)=mx+b
[tex]f(g(x))=m(2x+3)+b=2mx+3m+b=3x-8[/tex]
the follow equation system results:
[tex]2m=3 \\ 3m+b=-8[/tex]
[tex]m=\frac{3}{2}\\\\b=-\frac{25}{2}[/tex]
finally:
[tex]y=f(x)=\frac{3}{2}x-\frac{25}{2}[/tex]
now is time to calculate the inverse function:
[tex]y=\frac{3}{2}x-\frac{25}{2}=>2y+25=3x=>x=\frac{2}{3}y+\frac{25}{3}[/tex]
so
[tex]f^{-1}(x)=\frac{2}{3}x+\frac{25}{3}[/tex]
