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maxonik [38]
3 years ago
15

G(x)=-x + 4x h(x)=4x + 2 Find (g-h)(-4x) How do I answer this question

Mathematics
1 answer:
Digiron [165]3 years ago
4 0

Answer:

(g - h)(-4x) = 4x - 2

Step-by-step explanation:

This problem is one dealing with "composite functions."  We are given the definitions of functions g(x) and h(x) and are asked to find the difference between g and h, namely, what is left if we subtact h from g.  After having done that, we replace x in this composite function with the input (-4x).

The difference (g - h)(x) is as follows:  g(x) - h(x) = -x + 4x - [4x + 2].

If we simplify the algebra, we get g(x) - h(x) = -x + 4x - [4x + 2] = -x - 2.

Next, substitute -4x for x in this last result.  We get (g - h)(-4x) = 4x - 2.

Please note:  You might want to check out your g(x) = -x + 4x.  Normally we would write this as +3x.  

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so we have a table of values, with x,y coordinates, so let's use any two of those points to get the slope of the table and use the point-slope form to get its equation

~\hspace{2.7em}\stackrel{\textit{let's use}}{\downarrow }\qquad \stackrel{\textit{and this}}{\downarrow }\\\begin{array}{|lr|r|r|r|r|}\cline{1-6}x&0&1&2&3&4\\y&-1&3&7&11&15\\\cline{1-6}\end{array}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\(\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad(\stackrel{x_2}{4}~,~\stackrel{y_2}{15})

\stackrel{slope}{m}\implies\cfrac{\stackrel{rise}{\stackrel{y_2}{15}-\stackrel{y1}{3}}}{\underset{run}{\underset{x_2}{4}-\underset{x_1}{1}}}\implies \cfrac{12}{3}\implies 4\\\\\\% point-slope intercept\begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{4}(x-\stackrel{x_1}{1})\\\\\\y-3=4x-4\implies y = 4x-1\implies \blacktriangleright  y = 4x+(-1)\blacktriangleleft

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