Question

confirm that F and g are inverses by showing that f(g(x))=x and g(f(x))=x f(x)=x^3+4 and g(x)=3(sqrt of x-4)

Answer 1

we are given

`f(x)=x^3+4`

`g(x)=\sqrt[3]{x-4}`

Calculation of f(g(x)):

`f(x)=x^3+4`

replace x = g(x)

`f(g(x))=(g(x))^3+4`

we can plug g(x)

`f(g(x))=(\sqrt[3]{x-4})^3+4`

`f(g(x))=x-4+4`

`f(g(x))=x`

Calculation of g(f(x)):

we are given

`g(x)=\sqrt[3]{x-4}`

replace x =f(x)

`g(f(x))=\sqrt[3]{f(x)-4}`

we can replace f(x)

we get

`g(f(x))=\sqrt[3]{x^3+4-4}`

`g(f(x))=\sqrt[3]{x^3}`

`g(f(x))=x`

we can see that

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

so, f(x) and g(x) are inverse of each other..........Answer