Question

The function h(x) = (x+4)³ can be expressed in the form f(g(x)) where f(x) = x³, and g(x) is defined

below:
g(x)=

Answer 1

To express the function
`\displaystyle\sf h(x) = (x+4)^(3)` in the form
`\displaystyle\sf f(g(x))`, where
`\displaystyle\sf f(x) = x^(3)` and
`\displaystyle\sf g(x)` is the inner function, we need to determine
`\displaystyle\sf g(x)`.

Notice that
`\displaystyle\sf h(x)` is the cube of
`\displaystyle\sf (x+4)`. This suggests that
`\displaystyle\sf g(x)` is equal to
`\displaystyle\sf x+4`.

So,
`\displaystyle\sf g(x) = x+4`.

Now, to express
`\displaystyle\sf h(x)` as
`\displaystyle\sf f(g(x))`, we substitute
`\displaystyle\sf g(x) = x+4` into
`\displaystyle\sf f(x) = x^(3)`:

`\displaystyle\sf h(x) = f(g(x)) = f(x+4) = (x+4)^(3)`.

Therefore,
`\displaystyle\sf h(x)` can be expressed as
`\displaystyle\sf f(g(x))`, where
`\displaystyle\sf f(x) = x^(3)` and
`\displaystyle\sf g(x) = x+4`.