Question

X + 5For f(x) = 3x - 5 and g(x) =3find the following functions.a. (fog)(x); b. (g of)(x); c. (fog)(3); d. (gof)(3)

Answer 1

a. (fog)(x)

In this part, we need to evaluate f(x) in g(x), this means that we need to replace g(x) for x in f(x), this way:

$\begin{gathered} (f\circ g)(x)=f(g(x)) \\ (f\circ g)(x)=3(g(x))-5 \\ (f\circ g)(x)=3(\frac{x+5}{3})-5 \\ (f\circ g)(x)=x+5-5 \\ (f\circ g)(x)=x \end{gathered}$

It means (fog)(x)=x

b. (gof)(x)

In this part, we need to do a similar procedure but this time, evaluate g(x) in f(x):

$\begin{gathered} (g\circ f)(x)=g(f(x)) \\ (g\circ f)(x)=\frac{f(x)+5}{3} \\ (g\circ f)(x)=\frac{3x-5+5}{3} \\ (g\circ f)(x)=\frac{3x}{3} \\ (g\circ f)(x)=x \end{gathered}$

It means (gof)(x)=x too.

c. (fog)(3)

Evaluate the expression in the first part in 3.

$(f\circ g)(3)=3$

(fog)(3)=3

d. (gof)(3)

Evaluate the expression in the second part in 3.

$(g\circ f)(3)=3$

(gof)(3)=3