Composition of Functions: Finding g(f-1(x)) with Given Equations

[Darknes51986]

Homework Statement

Given: f(x)= 1/3x + 2 and g(x)= 2x²- x + 7

Find: g(f^-1(x))

Homework Equations

The Attempt at a Solution

x=1/3y + 2
1/3y= x - 2
y=(x-2)/(1/3)
y=3x-6= f^-1(x)

2(3x-6)² + (3x-6) +7
solved to get..
18x²-69x+71

 

[dacruick]

I got a different answer but your method is correct. You have a sign error somewhere.

 

[HallsofIvy]

2(36)- 6+ 7= 72+1= 73, not 71.

 

[dacruick]

g(x)= 2x² - x + 7

2(3x-6)² + (3x-6) + 7