Find the inverse of the function.

f(x) = x^3 + 5

Question

Find the inverse of the function.

f(x) = x^3 + 5

hang254 · Answer

@ganeshie8 @cwrw238

jdoe0001 · Answer

.... hmmm do you know how to find inverse functions?

hang254 · Answer

i think it is $$f^-1(x) = \sqrt[3]{x-5}$$

hang254 · Answer

to a certain extent

jdoe0001 · Answer

right, however   ... one sec

jdoe0001 · Answer

attachment

jdoe0001 · Answer

notice the graph of the resulting "expression"

do you think it will pass the "vertical line test" needed to have it as a function?

so, you can simplify the expression, it just won't give a "function  as defined"

jdoe0001 · Answer

so $\bf f(x) = x^3 + 5 $  has no inverse function

hang254 · Answer

oh, so i was incorrect.

hang254 · Answer

thanks! @jdoe0001

jdoe0001 · Answer

yw

agent0smith · Answer

"Find the inverse" to me means find the inverse, whether it's a function or not @jdoe0001

agent0smith · Answer

And x^3+5 is one to one and thus has an inverse which is a function...

agent0smith · Answer

https://www.google.com/search?q=(x-5)%5E(1%2F3)&oq=(x-5)%5E(1%2F3)&aqs=chrome..69i57j0l5.6401j0j7&sourceid=chrome&espv=210&es_sm=93&ie=UTF-8 inverse which is a function. Idk what your graph is @jdoe0001 but it's not correct.

agent0smith · Answer

@hang254 you were correct with $$\Large f^{-1}(x) = \sqrt[3]{x-5}$$

agent0smith · Answer

If a function passes the horizontal line test, as x^3+5 does, then it has an inverse which is a function.