Question

F(x)=x-3 g(x)=-0.5x for what interval is the value of (f-g)(x) negative?

Answer 1

Answer:

(-∞, 2)

Step-by-step explanation:

Given functions:

$\begin{cases} f(x)=x-3\\g(x)=-0.5x \end{cases}$

Function composition is an operation that takes two functions and produces a third function.

The composite function (f - g)(x) means to subtract function g(x) from function f(x):

$\begin{aligned}(f-g)(x) & = f(x)-g(x)\\& = (x-3)-(-0.5x)\\& = x-3+0.5x\\& = 1.5x-3\end{aligned}$

To find the interval for which (f - g)(x) is negative, set the new function to less than zero and solve the inequality:

$\begin{aligned}(f-g)(x) & < 0\\\implies 1.5x-3 & < 0\\1.5x & < 3\\x & < \dfrac{3}{1.5}\\x & < 2\end{aligned}$

Therefore, the interval for which (f - g)(x) is negative is (-∞, 2).

Learn more about composite functions here:

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brainly.com/question/27966754

Answer 2

$\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}$

Given:

▪ $\longrightarrow \sf{f(x)=x-3}$

▪ $\longrightarrow \sf{g(x)=-0.5x}$

$\large\leadsto$ Subtract the function g(x) from the function f(x), in order to find:

$\small\longrightarrow \sf{(f - g)(x)}$

$\large\leadsto$ Then, you get:

$\small\longrightarrow \sf{(f-g)(x) = x - 3 - (-0.5x)}$

$\small\longrightarrow \sf{(f-g)(x) = x - 3 + 0.5x}$

$\small\longrightarrow \sf{(f-g)(x) = 1.5x - 3}$

$\large\leadsto$ By definition, negative numbers are less than zero. Therefore, you can set up the following inequality:

$\longrightarrow \sf{1.52 - 3 < 0}$

Solve for x :

$\small\longrightarrow \sf{1.52 < 3}$

$\small\longrightarrow \sf{x < \dfrac{3}{1.5} }$

$\small\longrightarrow \sf{x < 2}$

$\small\longrightarrow \sf{= ( \infin,2)}$

$\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}$

$\boxed{\bm{( \infin,2)}}$