function f(x) is increasing exponential function of the form [tex]f(x)=a^x[/tex] passing through the point [tex](1,\frac{9}{2}).[/tex] So, [tex]f(1)=\frac{9}{2}\Rightarrow a^1=a=\frac{9}{2}[/tex] and function f(x) has the expression [tex]f(x)=(\frac{9}{2})^x;[/tex]
function g(x) is decreasing exponential function of the form [tex]g(x)=b^x[/tex] passing through the point [tex](-1,\frac{9}{2}).[/tex] So, [tex]g(-1)=\frac{9}{2}\Rightarrow b^{-1}=\frac{1}{b}=\frac{9}{2},[/tex] so [tex]b=\frac{2}{9}[/tex] and function g(x) has the expression [tex]g(x)=(\frac{2}{9})^x.[/tex]
