The function for the cost of materials to make a shirt is f(x) = x + 5, where x is the number of shirts. The function for the selling price of those shirts is g(f(x)), where g(x) = 5x + 6. Find the selling price of 18 shirts. (1 point)

Question

The function for the cost of materials to make a shirt is f(x) =   x + 5, where x is the number of shirts. The function for the selling price of those shirts is g(f(x)), where g(x) = 5x + 6. Find the selling price of 18 shirts. (1 point)

anonymous · Answer

So we know:
$$\eqalign{
&f(x)=x+5 \
&g(x)=5x+6 \
}$$
And they want us to find $g[f(18)]$ So let us derive a function, $h(x)=g[f(x)]$
$$h(x)=g[f(x)]=g(x+5)=5(x+5)+6=5x+25+6=5x+31$$
Now the function evaluated at 18 is:
$$h(18)=5(18)+31=90+31=121$$

anonymous · Answer

To check this, you can find $f(18)$ and plug that value in for $g(x)$:
$$f(18)=18+5=23$$
$$g(23)=5(23)+6=115+6=121$$

anonymous · Answer

Wait.. Wouldn't it be 30, not 31?

anonymous · Answer

Naw, $25+6=31$

anonymous · Answer

You're literally the best. 
I've been stuck on this forever.

anonymous · Answer

Haha I try Juli! Anytime :)