Mathematics
Algebra 2 needs all work shown

Question Description

Determine if f(x)=(2x+5)^3 and g(x)=x^1/3-5 over 2 are inverses by finding [f of g](x) and [g of f](x)

Final Answer

Remember the definition of an inverse function. If y = f(x) takes you from x to y, then the inverse function x = f-1(y) takes you back from y to x.

So let's find [f of g](x), in other words f(g(x)):

f(g(x)) = f([x^1/3 - 5]/2) 

= (2[x^1/3 - 5]/2 + 5)^3

Cancel those 2s:

= (x^1/3 - 5 + 5)^3

Now cancel the 5s:

= (x^1/3)^3

= x

Similarly if we find [g of f](x):

g(f(x)) = ([(2x+5)^3]^1/3 - 5)/2

Cancel the ^3 / ^1/3:

 g(f(x)) = (2x+5 - 5)/2

And the 5s:

g(f(x)) = 2x/2

= x


See what's happening? If you start with x, and apply the function f to it, you get f(x). But then if you apply g to that value f(x), you get back the original value x. And the same for g(x) - if you apply thr function f to that, you get back the original x than went in to g.

So the two functions are inverses of each other. If you apply one to x, you can get back the original x by applying the other function to your result.


x -> Apply f -> f(x) -> Apply g -> x

x -> Apply g -> g(x) -> Apply f -> x

iainharlow (1041)
UCLA

Anonymous
I was on a very tight deadline but thanks to Studypool I was able to deliver my assignment on time.

Anonymous
The tutor was pretty knowledgeable, efficient and polite. Great service!

Anonymous
Heard about Studypool for a while and finally tried it. Glad I did caus this was really helpful.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors