Question

find the domain and range of f(x)=x²-36/x-6.
x≠6​

Answer 1

Given ,

The function is

$\tt f(x) = \frac{ {(x)}^{2} - 36 }{x - 6}$

For f(x) to be defined ,

x- 6 ≠ 0

x ≠ 6

Therefore , Domain = R - {6}

Let , f(x) = y

Thus ,

$\tt \implies y = \frac{ {(x)}^{2} - 36}{x - 6}$

$\tt \implies y = \frac{ {(x)}^{2} - {(6)}^{2} }{x - 6}$

$\tt \implies y = \frac{(x + 6)(x - 6)}{(x - 6)}$

$\tt \implies y = x + 6$

$\tt \implies x = y - 6$

Since , x ≠ 6

Thus ,

y - 6 ≠ 6

y ≠ 12

Therefore , Range = R - {12}

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