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Calculus, 8th Edition,stewart; page 21 problem 32

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Find the domain of the function.

f(x) = (2x^3 - 5)/(x^2 + x - 6)

functions
domain-of-a-function

asked Jul 27, 2015 in CALCULUS by anonymous

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1 Answer

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Step:1

The function is $f(x)=\frac{2x^3-5}{x^2+x-6}$ .

All possible values of $\large x$ is domain of a function.

The denominator of the function should not be zero.

$x^2+x-6\neq 0$

$x^2+3x-2x-6\neq 0$

$x(x+3)-2(x+3)\neq 0$

$(x+3)(x-2)\neq 0$

$x+3\neq 0$ and $x-2\neq 0$

$x\neq -3$ and $x\neq 2$ .

Hence, the domain of function is set of all real numbers except $-3$ and $2$ .

The domain of the function is $(-\infty, -3 )\cup (-3, 2)\cup (2, \infty )$ .

Solution:

The domain of the function is $(-\infty, -3 )\cup (-3, 2)\cup (2, \infty )$ .

answered Jul 28, 2015 by dozey Mentor

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