Question

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Answer 1

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.