Fraternal functions
Suppose and . Find the value of that satisfies given that .
This is a modified high school problem.
The answer is 3.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Method 1:
f f ′ ( m ) = − 5
f ( 3 m − 2 g ( m ) ) = − 5
f ( 3 m − 2 m + 4 ) = − 5
4 ( 3 m − 2 m + 4 ) − 5 g ( 3 m − 2 m + 4 ) = − 5
4 ( 3 m − 2 m + 4 ) − 5 3 m − 2 m + 4 + 4 = − 5
4 m + 1 6 − ( 1 5 m − 1 0 ) m + 4 + 1 2 m − 8 = − 5
2 6 − 1 1 m 1 3 m − 4 = − 5
1 3 m − 4 = 5 5 m − 1 3 0
( 5 5 − 1 3 ) m = 1 3 0 − 4
4 2 m = 1 2 6
m = 4 2 1 2 6 = 3
Method 2:
f f ′ ( m ) = − 5
4 f ′ ( m ) − 5 g f ′ ( m ) = − 5
4 f ′ ( m ) − 5 f ′ ( m ) + 4 = − 5
f ′ ( m ) + 4 = 2 5 − 2 0 f ′ ( m )
2 1 f ′ ( m ) = 2 1
f ′ ( m ) = 1
3 m − 2 g ( m ) = 1
3 m − 2 m + 4 = 1
m + 4 = 3 m − 2
2 m = 6
m = 3