Question

If $f\left(x\right)=\frac{2x+5}{x^2+x+5}$, then $f\left[f\right(-1\left)\right]$ is equal to

• A. $\frac{149}{155}$
• B. $\frac{155}{147}$
• C. $\frac{155}{149}$
• D. $\frac{147}{155}$

Answer 1

The correct option is C $\frac{155}{149}$

Given expression is $f\left(x\right)=\frac{2x+5}{x^2+x+5}$

$\therefore f(-1)=\frac{2\times (-1)+5}{(-1{)}^2+(-1)+5}=\frac{3}{5}$

$\therefore f\left(f(-1)\right)=\frac{2\times \frac{3}{5}+5}{{\left(\frac{3}{5}\right)}^2+\frac{3}{5}+5}=\frac{155}{149}$