Which pair of functions is not a pair of inverse functions? A. f(x)= x+1/6 and g(x)= 6x-1 B. f(x)= x-4/19 and g(x)= 19x+4 C. f(x)= x5 and g(x)= 5√x D. f(x)= x/x + 20 and g(x)= 20x/x-1
Mathematics · Middle School · Tue Nov 03 2020
Answered on
f(g(x))=g(f(x))=x
then f and g are inverse functions.
A.
f(x) = \frac{x + 1}{6}f(x)=6x+1
g(x) = 6x - 1g(x)=6x−1
f(g(x)) = \frac{6x - 1 + 1}{6} = \frac{6x}{6} = xf(g(x))=66x−1+1=66x=x
B.
f(x) = \frac{x - 4}{19}f(x)=19x−4
g(x) = 19x + 4g(x)=19x+4
f(g(x)) = \frac{19x + 4 - 4}{19} = \frac{19x}{19} = xf(g(x))=1919x+4−4=1919x=x
C.
f(x) = {x}^{5}f(x)=x5
g(x) = \sqrt[5]{x}g(x)=5x
f(g(x)) = (\sqrt[5]{x})^{5} = xf(g(x))=(5x)5=x
D.
f(x) = \frac{x}{x + 20 }f(x)=x+20x
g(x) = \frac{20x}{x - 1}g(x)=x−120x
f(g(x)) = \frac{ \frac{20x}{x - 1} }{ \frac{20x}{x - 1} + 20} = \frac{20x}{40x - 20} = \frac{x}{2x - 1}f(g(x))=x−120x+20x−120x=40x−2020x=2x−1x
The correct answers ar A, B , C