Answer to Question #114469 in Calculus for Mohamed

Question

Find f(0),f(2),f(-2),f(3),f(√2 ), and f(3t) if :

a) f(x)=3x^2 -2

b) f(x)=√(x+1)

Answer 1

a) $f(x)=3x^2-2,$

$f(0)=3*0^2-2=-2$

$f(2)=3*2^2-2=3*4-2=10$

$f(-2)=3*(-2)^2-2=3*4-2=10$

$f(3)=3*3^2-2=3*9-2=25$

$f(\sqrt{2})=3*(\sqrt{2})^2-2=3*2-2=4$

$f(3t)=3*(3t)^2-2=3*9t^2-2=27t^2-2$

b) $f(x)=\sqrt{x+1},$

$f(0)=\sqrt{0+1}=1$

$f(2)=\sqrt{2+1}=\sqrt{3}$

$f(-2)=\sqrt{-2+1}=\sqrt{-1}$ is undetermined in real numbers

$f(3)=\sqrt{3+1}=\sqrt{4}=2$

$f(\sqrt{2})=\sqrt{\sqrt{2}+1}$

$f(3t)=\sqrt{3t+1}$