SOLUTION: Use composition of functions to show that the functions f(x)=4-5x and g(x)=4/5-1/5 x are inverse functions Carefully show that (fog)(x)=x and show that (gof)(x)=x.

Algebra ->  Functions -> SOLUTION: Use composition of functions to show that the functions f(x)=4-5x and g(x)=4/5-1/5 x are inverse functions Carefully show that (fog)(x)=x and show that (gof)(x)=x.       Log On


   

Question 745105: Use composition of functions to show that the functions
f(x)=4-5x and g(x)=4/5-1/5 x are inverse functions
Carefully show that (fog)(x)=x and show that (gof)(x)=x.
Found 2 solutions by sachi, stanbon:
Answer by sachi(548) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=4-5x and g(x)=4/5-1/5 x
(fog)(x)=x
or (fog)(x)=f(g(x))=f(4/5-1/5 x)=4-5(4/5-1/5 x)=4-(4-x)=4-4+x=x proved
and (gof)(x)=x.
(gof)(x)=g(f(x))=g(4-5x)=4/5-1/5(4-5x)=4/5-(4/5-x)=4/5-4/5+x=x

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=4-5x and g(x)=4/5-1/5 x are inverse functions
Carefully show that (fog)(x)=x and show that (gof)(x)=x.
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f(x) = 4-5x ; g(x) = (4-x)/5
------
fog(x) = f[g(x)] = f[(4-x)/5]
------
= 4-5[(4-x)/5]
= 4-(4-x)
= x
-----------------------
gof(x) = g[f(x)] = g[(4-5x)] = (4-[(4-5x))/5
-------
= (5x)/5
-------
= x
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Cheers,
Stan H.
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