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

We save the definition:

f (x) = \frac{2 x^{2} - 6 x + 2}{{(2 x - 3)}^{2}}

Let's evaluate the domain of

\frac{2 x^{2} - 6 x + 2}{{(2 x - 3)}^{2}}

For the expression

\frac{2 x^{2} - 6 x + 2}{{(2 x - 3)}^{2}}

to be defined, we must have:

{(2 x - 3)}^{2} \neq 0

{(2 x - 3)}^{2} \neq 0

is equivalent to:

2 x - 3 \neq 0

ⓘ We add

3

to both sides

2 x \neq 3

ⓘ Both sides are divided by

2

▶Domain of definition:

x \neq \frac{3}{2}

The numeric value of:

x \neq \frac{3}{2}

equals:

▷

x \neq 1.5