Chapter 10 - Exponents and Radicals - 10.1 Radical Expressions and Functions - 10.1 Exercise Set - Page 634: 33

$f(0)=1 ,\\\\ f(-1)=\sqrt{2} ,\\\\ f(-10)=\sqrt{101}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Substitute the given function value in $f(t)=\sqrt{t^2+1} .$ $\bf{\text{Solution Details:}}$ If $t=0 ,$ then \begin{array}{l}\require{cancel} f(t)=\sqrt{t^2+1} \\\\ f(0)=\sqrt{0^2+1} \\\\ f(0)=\sqrt{1} \\\\ f(0)=1 .\end{array} If $t=-1 ,$ then \begin{array}{l}\require{cancel} f(t)=\sqrt{t^2+1} \\\\ f(-1)=\sqrt{(-1)^2+1} \\\\ f(-1)=\sqrt{2} .\end{array} If $t=-10 ,$ then \begin{array}{l}\require{cancel} f(t)=\sqrt{t^2+1} \\\\ f(-10)=\sqrt{(-10)^2+1} \\\\ f(-10)=\sqrt{101} .\end{array} Hence, \begin{array}{l}\require{cancel} f(0)=1 ,\\\\ f(-1)=\sqrt{2} ,\\\\ f(-10)=\sqrt{101} .\end{array}

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