Write the inverse of 6x+8y=13 in f^-1(x) notation

Mathematics

1 answer:

Margarita [4]2 years ago

4 0

Answer:

-4x/3+13/6

Step-by-step explanation:

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First find the equation of the line that passes through the points B and C.
$B(4, -3) \\
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C(-4,3) \\
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Now plug the coordinates of the given points into the equation and check if they satisfy the equation.

$(0,0) \\
x=0 \\ y=0 \\ \Downarrow \\
0 \stackrel{?}{=} -\frac{3}{4} \times 0 \\
0 \stackrel{?}{=} 0 \\
0=0 \\
\hbox{the point lies on the line} \\ \\
(1,1) \\
x=1 \\ y=1 \\ \Downarrow \\
1 \stackrel{?}{=} -\frac{3}{4} \times 1 \\
1 \stackrel{?}{=} -\frac{3}{4} \\
1 \not= -\frac{3}{4} \\
\hbox{the point doesn't lie on the line}$

$
(1,-5) \\
x=1 \\ y=-5 \\ \Downarrow \\ -5 \stackrel{?}{=} -\frac{3}{4} \times 1 \\
-5 \stackrel{?}{=} -\frac{3}{4} \\
-5 \not= -\frac{3}{4} \\
\hbox{the point doesn't lie on the line} \\ \\
(6,-8) \\
x=6 \\ y=-8 \\ \Downarrow \\
-8 \stackrel{?}{=} -\frac{3}{4} \times 6 \\
-8 \stackrel{?}{=} -\frac{9}{2} \\
-8 \not= -\frac{9}{2} \\
\hbox{the point doesn't lie on the line}$

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