Question

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

Answer 1

ANSWER

1

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:

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