Question

Use f(x)=(2x+1)/(3x-2) and g(x)=5x-1 to find (gof)(x)

Answer 1

Answer:

From the functions f(x) and g(x) we have $(g\circ f)(x)=\frac{7(x+1)}{3x-2}$

Step-by-step explanation:

Given that the functions f is defined by $f(x)=\frac{2x+1}{3x-2}$

and g is $g(x)=5x-1$

To find the $(g\circ f)(x)$ :

$(g\circ f)(x)=g(f(x))$

$=g(\frac{2x+1}{3x-2})$

$=5(\frac{2x+1}{3x-2})-1$

$=\frac{10x+5}{3x-2}-1$

$=\frac{10x+5-1(3x-2)}{3x-2}$ ( by using the distributive property )

$=\frac{10x+5-3x+2}{3x-2}$

$=\frac{7x+7}{3x-2}$ ( adding the like terms )

$=\frac{7(x+1)}{3x-2}$

Therefore $(g\circ f)(x)=\frac{7(x+1)}{3x-2}$.