Question

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.

Answer 1

@Compassionate @johnweldon1993

Answer 2

Well we would just plug them into each other

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

and for the other

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

\[\large \color \red{\checkmark}\]

Answer 3

Thank you so much! I knew what I had to do (plug them into each other) but just wasn't sure how to do it

Answer 4

@johnweldon1993 could you help me on 1 more?

Answer 5

Sure, apologies in advance for any delays as I am doing work at the same time lol

Answer 6

Its fine :-)

Answer 7

f(x) = 3x + 6, g(x) = 2x^2

Find (fg)(x).

2x^2 + 3x + 6

6x + 12

6x^2 + 12x

6x3 + 12x^2

Answer 8

Okay, so noice how the grouping is different here

\[\large (fg)(x)\] so this means we need to multiply our 2 functions...

\[\large f = 3x + 6\]
\[\large g(x) = 2x^2\]

so

\[\large (fg) = (3x + 6) \times (2x^2)\]

Answer 9

6x^3+12x^2 ?

Answer 10

Correct indeed!