Chapter 11.9, Problem 38WE

To determine

Find the value of function $f\left(\sqrt{3}+2\right)$ .

Answer to Problem 38WE

  $\boxed{f\left(\sqrt{3}+2\right)=-\sqrt{3}-10}$

Explanation of Solution

Given information:

  $f\left(x\right)=x^2-5x-7$

  $f\left(x\right)=x^2-5x-7$

Now putting value of $f\left(\sqrt{3}+2\right)$ in the equation $f\left(x\right)=x^2-5x-7$ .

  $\begin{array}{l}f\left(\sqrt{3}+2\right)={\left(\sqrt{3}+2\right)}^2-5\left(\sqrt{3}+2\right)-7\\ f\left(\sqrt{3}+2\right)=\left(3+4\sqrt{3}+4\right)-5\sqrt{3}-10-7\\ f\left(\sqrt{3}+2\right)=4\sqrt{3}-5\sqrt{3}-10\\ \boxed{f\left(\sqrt{3}+2\right)=-\sqrt{3}-10}\end{array}$