Answer:
From the functions f(x) and g(x) we have [tex](g\circ f)(x)=\frac{7(x+1)}{3x-2}[/tex]
Step-by-step explanation:
Given that the functions f is defined by [tex]f(x)=\frac{2x+1}{3x-2}[/tex]
and g is [tex]g(x)=5x-1[/tex]
To find the [tex](g\circ f)(x)[/tex] :
[tex](g\circ f)(x)=g(f(x))[/tex]
[tex]=g(\frac{2x+1}{3x-2})[/tex]
[tex]=5(\frac{2x+1}{3x-2})-1[/tex]
[tex]=\frac{10x+5}{3x-2}-1[/tex]
[tex]=\frac{10x+5-1(3x-2)}{3x-2}[/tex] ( by using the distributive property )
[tex]=\frac{10x+5-3x+2}{3x-2}[/tex]
[tex]=\frac{7x+7}{3x-2}[/tex] ( adding the like terms )
[tex]=\frac{7(x+1)}{3x-2}[/tex]
Therefore [tex](g\circ f)(x)=\frac{7(x+1)}{3x-2}[/tex].
