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

Cabiolab
2021-09-16
Answered

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

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timbalemX

Answered 2021-09-17
Author has **108** answers

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.

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

B=6

Hence, the value of B is equal to 6.

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