Question

verify that the function f(X)=x^3-7 and g(X)=3sqrt x+7 are inverse of each other

Answer 1

do you know how to solve for f(g(x))?

Answer 2

yes

Answer 3

good. first, let me tell you the concept

they are inverse if:

f(g(x)) = g(f(x))

so to verify...you need to solve for f(g(x)) and g(f(x)) and see if they are equal

does that help?

Answer 4

i try first , k?

Answer 5

sure

Answer 6

f[g(X)]=f(3sqr [x+7]]

Answer 7

yes go on... substitute \(3\sqrt{x+7}\) into the x of x^3 - 7

Answer 8

f(g(X))=(3sqrt x+7)^3 -7 , i dont no how to solve this

Answer 9

one question first... is that \[3\sqrt{x+7}\]or \[3\sqrt x + 7\]

Answer 10

the first one

Answer 11

oh cool.

anyway...try solving g(f(x)) first if you're stuck here. you dont know...it might look like that too

Answer 12

Actually you can just solve for f(X)=x^3-7
Let y=x^3-7
y+7=x^3
\[\sqrt[3]{y+7}=x\]
\[f^{-1}(x)=\sqrt[3]{x+7}=g(x)\]