1 Answer

CephBirk · Answer 1 · 2021-10-27T20:48:35+0000

Given that the functions
f(x)=x+4 and
g(x)=x^(3)

We need to determine the value of the function
$(g \ {\circ} f)(-3)$

First, we shall determine the composition of the function
$(g \circ f)(x)$

Function
$(g \circ f)(x)$ :

Let us determine the function
$(g \circ f)(x)$

Thus, we have;

$(g \circ f)(x)=g[f(x)]$

=g[x+4]

=(x+4)^3

$(g \circ f)(x)=x^3+3x^2(4)+3x(4)^2+(4)^3$

$(g \circ f)(x)=x^3+12x^2+48x+64$

Thus, the function is
$(g \circ f)(x)=x^3+12x^2+48x+64$

Value of the function
$(g \ {\circ} f)(-3)$ :

The value of the function can be determined by substituting x = -3 in the function
$(g \circ f)(x)=x^3+12x^2+48x+64$

Thus, we have;

$(g \circ f)(-3)=(-3)^3+12(-3)^2+48(-3)+64$

Simplifying the terms, we get;

$(g \circ f)(-3)=-27+12(9)+48(-3)+64$

$(g \circ f)(-3)=-27+108-144+64$

$(g \circ f)(-3)=1$

Thus, the value of the function
$(g \ {\circ} f)(-3)$ is 1.

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