SOLUTION: Find the functions f ○ g and g ○ f.
f(x)=5x-9 ; g(x)=1/5(x+9)
(f ○ g)(x) =
(g ○ f)(x) =
Algebra.Com
Question 1031181: Find the functions f ○ g and g ○ f.
f(x)=5x-9 ; g(x)=1/5(x+9)
(f ○ g)(x) =
(g ○ f)(x) =
Found 2 solutions by stanbon, Cromlix:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the functions f ○ g and g ○ f.
f(x)=5x-9 ; g(x)=1/5(x+9)
(f ○ g)(x) = f[g(x)] = f[(1/5)(x+9)] = 5[(1/5)(x+9)]-9 = x
(g ○ f)(x) = g[f(x)] = g[5x-9] = (1/5)(5x-9+9) = x
------
Comment:: That means f and g are inverse to one another.
------
Cheers,
Stan H.
-----------
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
f(x) = 5x - 9
g(x) = 1/5(x + 9)
(f o g)(x) = 5(1/5(x + 9) - 9)
(f o g)(x) = (x + 9)- 9
(f o g)(x) = x + 9 - 9
(f o g)(x) = x
.........
(g o f)(x) = 1/5(5x - 9 + 9)
g o f)(x) = 1/5(5x)
(g o f)(x) = x
.........
The reason for the answer of 'x'
in both cases is f(x) is the inverse
of g(x) and g(x) is the inverse of f(x)
Hope this helps :-)
RELATED QUESTIONS
Find the functions f ○ g and g ○ f.
f(x) = √x-8; g(x)= x^2
(f... (answered by Cromlix)
Find the rules for the composite functions f ○ g and g ○ f.
f(x) = 4x^2 +... (answered by Boreal)
Use the functions f(x) = 2x +7, g(x) = x squared + 3x, and h(x) = 1/x-7 to find each of... (answered by funmath)
Given
f(x) = 2x2 + 1
and
g(x) = 8x − 9,
find the following.
(a)... (answered by stanbon)
If we have the following functions:
f(x) = 3x – 2 and g(x) = x2 – 2x find the... (answered by eperette)
If f(x) = 2x + 1 and g(x) = x^2, what is f ○ g? What is g ○... (answered by rothauserc)
Find the rules for the composite functions f ○ g and g ○ f
f(x) = 8x^2 +... (answered by Boreal)
Use f(x) = 4x − 2 and g(x) = 5 − x^2 to evaluate the expression.
(a) (f... (answered by stanbon)
For the given functions f, g and h, find f○g○h and state the exact domain of... (answered by solver91311)