Question

Evaluate the function f(x) at the given numbers (correct to six decimal places).

f(x) = x^2 − 5x/x^2-x-20


x = 5.5, 5.1, 5.05, 5.01, 5.005, 5.001, 4.9, 4.95, 4.99, 4.995, 4.999

Answer 1

The values of given function are shown in the below table.

Explanation:

The given function is

`f(x)=(x^2-5x)/(x^2-x-20)`

Simplify the given function.

`f(x)=(x(x-5))/(x^2-5x+4x-20)`

`f(x)=(x(x-5))/(x(x-5)+4(x-5))`

`f(x)=(x(x-5))/((x+4)(x-5))`

Cancel out the common factor.

`f(x)=(x)/(x+4)`

Substitute x=5.5 in the above equation.

`f(5.5)=(5.5)/(5.5+4)`

`f(5.5)=(5.5)/(9.5)`

`f(5.5)=0.57894736842`

`f(5.5)\approx 0.578947`

Similarly find the value for all values of x.

The values of given function are shown in the below table.