Question

If the fuction $f: R \rightarrow R$ be given by $f(x)=x^2+2$ and $g: R \rightarrow R$ be given by $g(x)=\frac{x}{x-1}, x \neq 1$, find fog and $g$ and hence find fog (2) and gof $(-3)$.

Answer 1

SOLUTION : $f: R \rightarrow R, f(x)=x^2+2, g: R \rightarrow R, g(x)=\frac{x}{x-1}, x \neq 1$

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

$f \circ g(x)=\left(\frac{x}{x-1}\right)^2+2  g \circ f(x)=\frac{x^2+2}{x^2+1} \\$

$f \circ g(2)=4+2=6  g \circ f(-3)=\frac{9+2}{9+1}=\frac{11}{10}$