Find the domain of each of the following. (a) f(x) = (√(x -...

Find the domain of each of the following. (a) $f(x) = \frac{\sqrt{x - 1}}{x - 7}$ (b) $g(x) = -9x^6 - 4x^5 + 9x^4 - 6$ (c) $h(x) = \frac{x^2 - 81}{x^2 - 2x - 99}$ (d) $y = \sqrt{-6x - 7}$

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Transcript

00:01 We have been given a piecewise function f of x.

00:03 We have been given a piecewise function f of x, which is defined as absolute value of x if minus 2 is less than or equal to x is less than 0 and x cube if x is greater than 0.

00:19 So first we need to find the domain of this function, which will be x is such that x is greater than or equal to minus 2 and x is not equal to 0.

00:32 So we can also write this as the union of the intervals minus infinity to minus 2 and 0 to positive infinity...

Question

Find the domain of each of the following. (a) \(f(x) = \frac{\sqrt{x - 1}}{x - 7}\) (b) \(g(x) = -9x^6 - 4x^5 + 9x^4 - 6\) (c) \(h(x) = \frac{x^2 - 81}{x^2 - 2x - 99}\) (d) \(y = \sqrt{-6x - 7}\)

Question

Find the domain of each of the following. (a) \(f(x) = \frac{\sqrt{x - 1}}{x - 7}\) (b) \(g(x) = -9x^6 - 4x^5 + 9x^4 - 6\) (c) \(h(x) = \frac{x^2 - 81}{x^2 - 2x - 99}\) (d) \(y = \sqrt{-6x - 7}\)

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