Question

. Let f(x) = x2 and g(x) = x − 3. Evaluate (g ∘ f)(−2). 1 7 20 −20

Answer 1

1

Step-by-step explanation

The given functions are:

`f(x) = {x}^(2)`

and

`g(x) = x - 3`

`(g \circ \: f)(x) = f(g(x))`

`(g \circ \: f)(x) = g( {x}^(2) )`

`(g \circ \: f)(x) = {x}^(2) - 3`

We substitute x=-2 to obtain;

`(g \circ \: f)( - 2) = {( - 2)}^(2) - 3`

We simplify to obtain:

`(g \circ \: f)( - 2) = 4- 3`

`(g \circ \: f)( - 2) = 1`

The first choice is correct.

Answer 2

For this case we have the following functions:

`f (x) = x ^ 2\\g (x) = x-3`

We must find
`(g_ {0} f) (x)`

By definition we have to:

`(g_ {0} f) (x) = g (f (x))`

So:

`g (f (x)) = (x ^ 2) -3 = x ^ 2-3`

We must evaluate the composite function for
`x = -2`

`g (f (-2)) = (- 2) ^ 2-3 = 4-3 = 1`

ANswer:

`g (f (-2)) = 1`