Question

Dado f (x)=3x-2, calcule
a) f-1 (x)
b) e-1 (-1)
c) f-1(0)
d) f -1 (3)
e) f-1(4)
f) f) -1 (-2)

Answer 1

Calculando a inversa $f^{-1}$

$f(x)=3x-2$

$x=3y-2 \iff 3y=x+2 \iff y=\dfrac{x+2}{3}$

$f^{-1}=\dfrac{x+2}{3}$

a) $f^{-1}(x)=\dfrac{x+2}{3}$

b) $f^{-1}(-1)=\dfrac{-1+2}{3}=\dfrac{1}{3}$

c) $f^{-1}(0)=\dfrac{0+2}{3}=\dfrac{2}{3}$

d) $f^{-1}(3)=\dfrac{3+2}{3}=\dfrac{5}{3}$

e) $f^{-1}(4)=\dfrac{4+2}{3}=\dfrac{6}{3}=2$

f) $f^{-1}(-2)=\dfrac{-2+2}{3}=\dfrac{0}{3}=0$