# If f(x)=\frac{2x+B}{x-3} and f(5)=8, what is the value of B

If $f\left(x\right)=\frac{2x+B}{x-3}$ and f(5)=8, what is the value of B
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A function is a relation that maps each value in its domain to exactly one value in its range. A rational function is a function that is a ratio of two polynomials.
The given function is a rational function as it is a ratio of two degree-one polynomials. The value of a function at a point are obtained by substituting the point in the function definition.
The given function definition is $f\left(x\right)=\frac{2x+B}{x-3}$ and f(5)=8. Hence, substitute x=5 in function definition and equate it to 8
$f\left(x\right)=\frac{2x+B}{x-3}$
$f\left(5\right)=8$
$8=\frac{2\cdot 5+B}{5-3}$
$8=\frac{10+B}{2}$
$10+B=16$
$10+B-10=16-10$
B=6
Hence, the value of B is equal to 6.