+0

Let \displaystyle f(x) = \frac{1}{x-3} and \displaystyle g(x) = \frac{1}{x-7}. Then the domain of f\circ g is equal to all reals except for

+3
319
1

Let \displaystyle f(x) = \frac{1}{x-3} and \displaystyle g(x) = \frac{1}{x-7}. Then the domain of f\circ g is equal to all reals except for two values, a and b with a

Guest Sep 15, 2014

#1
+91919
+13

Let \displaystyle f(x) = \frac{1}{x-3} and \displaystyle g(x) = \frac{1}{x-7}. Then the domain of f\circ g is equal to all reals except for two values, a and b with a

$$\\Let \displaystyle f(x) = \frac{1}{x-3} \quad and \quad \displaystyle g(x) = \frac{1}{x-7}. \\\\ \mbox{Then the domain of f\circ g is equal to all reals except for two values, a and b with a }$$

$$\\f \circ g=\dfrac{1}{\frac{1}{x-7}-3}\\\\ =\dfrac{1}{\frac{1-3(x-7)}{x-7}}\\\\\\ =\dfrac{1}{\frac{-3x+22}{x-7}}\\\\\\ =1 \div \frac{-3x+22}{x-7}\\\\ =1 \times \frac{x-7}{-3x+22}\\\\ =\frac{x-7}{22-3x}\\\\$$

NOW     x cannot equal to 7 or 22/3  because you cannot divide by zero!

$$x \in R \quad where \;x\ne7 \;and\;x\ne \frac{22}{3}$$

Melody  Sep 16, 2014
Sort:

#1
+91919
+13

Let \displaystyle f(x) = \frac{1}{x-3} and \displaystyle g(x) = \frac{1}{x-7}. Then the domain of f\circ g is equal to all reals except for two values, a and b with a

$$\\Let \displaystyle f(x) = \frac{1}{x-3} \quad and \quad \displaystyle g(x) = \frac{1}{x-7}. \\\\ \mbox{Then the domain of f\circ g is equal to all reals except for two values, a and b with a }$$

$$\\f \circ g=\dfrac{1}{\frac{1}{x-7}-3}\\\\ =\dfrac{1}{\frac{1-3(x-7)}{x-7}}\\\\\\ =\dfrac{1}{\frac{-3x+22}{x-7}}\\\\\\ =1 \div \frac{-3x+22}{x-7}\\\\ =1 \times \frac{x-7}{-3x+22}\\\\ =\frac{x-7}{22-3x}\\\\$$

NOW     x cannot equal to 7 or 22/3  because you cannot divide by zero!

$$x \in R \quad where \;x\ne7 \;and\;x\ne \frac{22}{3}$$

Melody  Sep 16, 2014

24 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details