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

Question

asked Sep 17, 2020 34.0k views

2 Answers

Bogdacutu · Answer 1 · 2020-09-18T09:49:24+0000

ANSWER

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.

Fczbkk · Answer 2 · 2020-09-24T04:10:17+0000

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

ANswer: