5.14
Znajdź funkcję liniową f taką, że:
f(2x-1)=5x+3
Niech
f(x) = a x + b
zatem
f( 2x - 1) = a*( 2x -1) + b = 2a x - a + b
2a x - a + b = 5x + 3
czyli
2a = 5
- a + b = 3
----------------
a = 2,5
-2,5 + b = 3
----------------------
b = 5,5
============
Odp. f(x) = 2,5 x + 5,5
==========================
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Niech
f(x) = a x + b
zatem
f( 2x - 1) = a*( 2x -1) + b = 2a x - a + b
zatem
2a x - a + b = 5x + 3
czyli
2a = 5
- a + b = 3
----------------
a = 2,5
-2,5 + b = 3
----------------------
a = 2,5
b = 5,5
============
Odp. f(x) = 2,5 x + 5,5
==========================