Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = x3 + 4 and g(x) = Cube root of quantity x minus four.

Question

03-12-2016
Mathematics

Answered

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = x3 + 4 and g(x) = Cube root of quantity x minus four.

Verified Answer :

Related Questions

Read the following story and determine if the statements on the following page are true or false Change each sentence thats false to make it true Un revelación

If one parent is heterozygous white Ww and the other is homozygous black ww give the phenotype and genotype ratios for this cross

If you put parentheses around a negative number does it turn positive Because I dont understand how 47 equals 3 We have to diagram it with integer tiles and I d

Painting is commonly thought of as synonymous with art because a we see many examples of it in everyday life and in museums b many are eyecatching with the use

Help me with this problem please Xbcd solve for c

374000 in standard form

What type of writing would most likely include a call to action encouraging the reader to act in some way a narrative essay b expository essay c persuasive essa

8 Who of the following wrote a morality play that could be likened to Star Wars and Lord of the Rings a William Byrd b Guillaume de Machaut c Hildegard von Bing

According to what agreement would the United States have to declare war against any nation that attacked Great Britain AWarsaw Pact BMarshall Plan CDeclaration

marsupials are found in north america and australia but they would not have been able to swim across the ocean according to scientists how did this group of org

miriyu miriyu · Answer 1 · 2016-12-03T21:24:03-05:00

f(x) = x³ + 4 and g(x) = ∛(x - 4)

so, the first thing the question asks of you is to see that f(g(x)) = x. try it out, plugging g(x) in as the x-variable in the first equation:

f(g(x)) = (∛(x - 4))³ + 4

they were merciful in writing this problem, and thankfully your cube roots cancel out and don't cause you any trouble. continue solving:

f(g(x)) = (∛(x - 4))³ + 4 ... cube root and exponent cancel
f(g(x)) = x - 4 + 4 ... simplify
f(g(x)) = x

so, yep. that one worked. try out the second half of the question: g(f(x)) = x

g(f(x)) = ∛((x³ + 4) - 4) ... simplify inside your radical, cancelling out the 4s
g(f(x)) = ∛(x³) ... the cube root of x³ is x itself, so:
g(f(x)) = x

and there you are. you've confirmed that these are inverses.

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.f(x) = x3 + 4 and g(x) = Cube root of quantity x minus four.

Verified Answer :

Related Questions

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = x3 + 4 and g(x) = Cube root of quantity x minus four.