Question

Find ( f o g) (x) when f (x) = x^2+6x+5 and g(x)=1/x+1

Answer 1

Answer:

$(f\circ g)(x)=\frac{1}{x^{2}}+\frac{8}{x}+12$

Step-by-step explanation:

Given that $f (x) = x^{2}+6x+5$ and $g(x)=\frac{1}{x}+1$ are the functions.

To find $(f\circ g)(x)$ with the given two functions. ie., to find the composite function of f(x) and g(x) which is denoted by $(f\circ g)(x)$

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

                 $=f(\frac{1}{x}+1)$

                  $=({\frac{1}{x}+1})^{2}+6\times ({\frac{1}{x}+1})+5$

                   $=\frac{1}{x^{2}}+\frac{2}{x}+1+\frac{6}{x}+6+5$

                     $=\frac{1}{x^{2}}+\frac{8}{x}+12$

Therefore $(f\circ g)(x)=\frac{1}{x^{2}}+\frac{8}{x}+12$

Therefore the composite function of f(x) and g(x) is  $(f\circ g)(x)=\frac{1}{x^{2}}+\frac{8}{x}+12$