Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Sure! Let's solve for each function with the specified inputs individually:
1. Evaluating [tex]\( f(-2) \)[/tex]:
The function [tex]\( f(x) \)[/tex] is given by:
[tex]\[ f(x) = \sqrt{-6x + 19} \][/tex]
Plugging [tex]\( x = -2 \)[/tex] into the function, we get:
[tex]\[ f(-2) = \sqrt{-6(-2) + 19} = \sqrt{12 + 19} = \sqrt{31} \][/tex]
Therefore:
[tex]\[ f(-2) = 5.5677643628300215 \][/tex]
2. Evaluating [tex]\( g(-3) \)[/tex]:
The function [tex]\( g(x) \)[/tex] is given by:
[tex]\[ g(x) = \frac{x}{x^2 + 15} \][/tex]
Plugging [tex]\( x = -3 \)[/tex] into the function, we get:
[tex]\[ g(-3) = \frac{-3}{(-3)^2 + 15} = \frac{-3}{9 + 15} = \frac{-3}{24} = -\frac{1}{8} \][/tex]
Simplified, we have:
[tex]\[ g(-3) = -0.125 \][/tex]
3. Evaluating [tex]\( h\left(-\frac{1}{4}\right) \)[/tex]:
The function [tex]\( h(x) \)[/tex] is given by:
[tex]\[ h(x) = -18 + |12x| \][/tex]
Plugging [tex]\( x = -\frac{1}{4} \)[/tex] into the function, we get:
[tex]\[ h\left(-\frac{1}{4}\right) = -18 + \left|12 \left(-\frac{1}{4}\right)\right| = -18 + \left|-3\right| = -18 + 3 = -15 \][/tex]
Therefore:
[tex]\[ h\left(-\frac{1}{4}\right) = -15.0 \][/tex]
So the simplified answers are:
[tex]\[ \begin{array}{c} f(-2) = 5.5677643628300215 \\ g(-3) = -0.125 \\ h\left(-\frac{1}{4}\right) = -15.0 \end{array} \][/tex]
1. Evaluating [tex]\( f(-2) \)[/tex]:
The function [tex]\( f(x) \)[/tex] is given by:
[tex]\[ f(x) = \sqrt{-6x + 19} \][/tex]
Plugging [tex]\( x = -2 \)[/tex] into the function, we get:
[tex]\[ f(-2) = \sqrt{-6(-2) + 19} = \sqrt{12 + 19} = \sqrt{31} \][/tex]
Therefore:
[tex]\[ f(-2) = 5.5677643628300215 \][/tex]
2. Evaluating [tex]\( g(-3) \)[/tex]:
The function [tex]\( g(x) \)[/tex] is given by:
[tex]\[ g(x) = \frac{x}{x^2 + 15} \][/tex]
Plugging [tex]\( x = -3 \)[/tex] into the function, we get:
[tex]\[ g(-3) = \frac{-3}{(-3)^2 + 15} = \frac{-3}{9 + 15} = \frac{-3}{24} = -\frac{1}{8} \][/tex]
Simplified, we have:
[tex]\[ g(-3) = -0.125 \][/tex]
3. Evaluating [tex]\( h\left(-\frac{1}{4}\right) \)[/tex]:
The function [tex]\( h(x) \)[/tex] is given by:
[tex]\[ h(x) = -18 + |12x| \][/tex]
Plugging [tex]\( x = -\frac{1}{4} \)[/tex] into the function, we get:
[tex]\[ h\left(-\frac{1}{4}\right) = -18 + \left|12 \left(-\frac{1}{4}\right)\right| = -18 + \left|-3\right| = -18 + 3 = -15 \][/tex]
Therefore:
[tex]\[ h\left(-\frac{1}{4}\right) = -15.0 \][/tex]
So the simplified answers are:
[tex]\[ \begin{array}{c} f(-2) = 5.5677643628300215 \\ g(-3) = -0.125 \\ h\left(-\frac{1}{4}\right) = -15.0 \end{array} \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.