Question

Let f(x) = x^2 and g(x) = x + 5, find: a. (f o g)(x)= b. ( g o f)(x)= c. (f o g)(5)= d. (g o f)(5)=

Answer 1

Solution:

Given the functions;

$f(x)=x^2,g(x)=x+5$

(a)

$\begin{gathered} (f\circ g)(x)=f(g(x)) \\ \\ (f\circ g)(x)=f(x+5) \\ \\ (f\circ g)(x)=(x+5)^2 \\ \\ (f\circ g)(x)=x^2+10x+25 \end{gathered}$

(b)

$\begin{gathered} (g\circ f)(x)=g(f(x)) \\ \\ (g\circ f)(x)=g(x^2) \\ \\ (g\circ f)(x)=x^2+5 \end{gathered}$

(c)

$\begin{gathered} (f\circ g)(x)= x^{2}+10x+25 \\ \\ (f\circ g)(5)=5^2+10(5)+25 \\ \\ (f\circ g)(5)=100 \end{gathered}$

(d)

$\begin{gathered} (g\circ f)(x)= x^{2}+5 \\ \\ (g\circ f)(5)=5^2+5 \\ \\ (g\circ f)(5)=30 \end{gathered}$