Question

Find the domain of the real valued function f(x) =
2x2-5x+7
(x-1)(x-2)(x-3)​

Answer 1

Correct question:

Find the domain of the real-valued function

$f(x) = \frac{2x^2 - 5x +7}{(x-1)(x-2)(x-3)}$

The domain of the real-valued function $f(x) = \frac{2x^2 - 5x +7}{(x-1)(x-2)(x-3)}$ is R - {1,2,3}

Given:

$f(x) = \frac{2x^2 - 5x +7}{(x-1)(x-2)(x-3)}$

To Find:

The domain of the real-valued function $f(x) = \frac{2x^2 - 5x +7}{(x-1)(x-2)(x-3)}$ =?

Solution:

We have to find the domain of the given function f(x), for this, we need to determine the values of x for which the function is defined.

The function f(x) is defined for all values of x except those values that make the denominator zero because anything defined by 0 is undefined.

So, (x-1)(x-2)(x-3) must not be equal to 0.

(x-1)(x-2)(x-3) ≠ 0

(x-1) ≠ 0, (x-2) ≠ 0, and (x-3) ≠ 0

x ≠ 1, x ≠ 2, and x ≠ 3.

Therefore, the function f(x) is defined for all real numbers except 1, 2, and 3.

The domain of the real-valued function $f(x) = \frac{2x^2 - 5x +7}{(x-1)(x-2)(x-3)}$ is R - {1,2,3}

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