What is the inverse of the function f(x) = 2x – 10?

Mathematics

1 answer:

noname [10]2 years ago

7 0

Answer:

The inverse f-1(x) = ( x + 10)/2.

Step-by-step explanation:

f(x) = 2x - 10

Find x in terms of f(x):

2x = f(x) + 10

x = (f(x) + 10))/ 2

Replace x by the inverse f-1(x) and f(x) by x:

f-1(x) = (x + 10)/2.

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Given that f(x) = x/(x - 3) and g(x) = 1/x and the application of function operators, f ° g (x) = 1/(1 - 3 · x) and the domain of the resulting function is any real number except x = 1/3.

<h3>How to analyze a composed function</h3>

Let be f and g functions. Composition is a binary function operation where the variable of the former function (f) is substituted by the latter function (g). If we know that f(x) = x/(x - 3) and g(x) = 1/x, then the composed function is:

$f\,\circ\,g \,(x) = \frac{\frac{1}{x} }{\frac{1}{x}-3}$

$f\,\circ\,g\,(x) = \frac{\frac{1}{x} }{\frac{1-3\cdot x}{x} }$

$f\,\circ\,g\,(x) = \frac{1}{1-3\cdot x}$

The domain of the function is the set of x-values such that f ° g (x) exists. In the case of rational functions of the form p(x)/q(x), the domain is the set of x-values such that q(x) ≠ 0. Thus, the domain of f ° g (x) is $\mathbb{R} - \{\frac{1}{3} \}$ .