The constant c is 4.8 or [tex]\frac{24}{5}[/tex]
Solution:
Given that function G is defined by:
[tex]G(x) = c + 6 \div x\\\\G(x) = c + \frac{6}{x}[/tex]
where c is a constant
The above function means that for every input x the output is g(x)
The graph of G passes through the point (5, 6)
To find c when graph passes through (5, 6)
So here, x = 5 and G(x) = 6
Substitute the above values in given function of G(x)
[tex]G(x) = c + \frac{6}{x}\\\\6 = c + \frac{6}{5}\\\\6 = \frac{5c+6}{5}\\\\30 = 5c + 6\\\\5c + 6 = 30\\\\5c = 30 - 6\\\\5c = 24\\\\c = \frac{24}{5} = 4.8[/tex]
Thus c is 4.8 or [tex]\frac{24}{5}[/tex]
