Homework Help: Math Analysis

Posted by Emily on Saturday, October 24, 2009 at 8:42pm.

6. Prove that f(x) = (3/4)x^4 + 2 and g(x) = (4sqrt(108x-216))/3 are inverses.

I know you solve it with composite functions f(g(x)) and g(f(x)), and I solved f(g(x)), but I can't seem to solve g(f(x)) to equal x, like it should. Can someone show me how to solve this? Thanks :)

Math Analysis - Emily, Saturday, October 24, 2009 at 8:43pm
The 4 in front of the sqrt is like the 4th root, like 3sqrt(... is the cubed root, etc.
Math Analysis - jim, Saturday, October 24, 2009 at 9:08pm
You probably took a wrong turn in what was included inside the fourth root. Easy turn to miss. :-)

f(x)=(3/4)x^4

g(x)= ((108((3/4)x^4 + 2)-216)^(1/4))/3

= ((81x^4 + 216 -216)^1/4) /3

= ((81x^4)^1/4) /3

= 81^(1/4)x^(1/4) /3

= 3 x / 3

= x
Math Analysis - Emily, Saturday, October 24, 2009 at 9:44pm
Ohhhhh, I think I get it now. Thanks jim! :D :D

Answer this Question

Related Questions

math- precalculus - Help please! I can't seem to get x as the answer to ...
Composite Functions - Find the composite functions for the given functions. (6 ...
Math - Inverse Functions - Find the inverses of the following functions. y = 3(x...
math - how to you find a composite function form of y in this problem? y = 1/[(x...
math-please I really need help!!!!! - Consider the functions f(x)=2x+8/x+6; g(x...
Math ( composite functions ) - I need some help with composite functions where ...
Very easy math - my teacher told me that the inverse of addition was subtraction...
CALCULUS - show that f(x) = x^2-1 (x is greater than and equal to 0) and g(x) = ...
Math Analysis - Let f(x)= x^3, g(x) = sqrt x, h(x) = x-4, and j(x)= 2x. Express ...
Functions - consider the functions g(x)=(4-x^2)^0.5 and h(x)=(x^2)-5. find the ...

For Further Reading

First Name:
School Subject:
Answer: