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Furkat [3]
3 years ago
5

F (x) = -3 + 7. Find the inverse of f(x) and its domain.

Mathematics
1 answer:
iragen [17]3 years ago
8 0

Note: Your function is missing some information. It seems your function is

f\left(x\right)=\frac{-3}{x}+7.

So, I am solving the question based on the function f\left(x\right)=\frac{-3}{x}+7,  because it would still solve your query.

Answer:

Please see the explanation.

Step-by-step explanation:

Given the function

f\left(x\right)=\frac{-3}{x}+7

A function g is the inverse of a function f for y = f(x), x=g(y)

y=\frac{-3}{x}+7

Replace x with y

x=\frac{-3}{y}+7

solve for y

y=-\frac{3}{x-7}

so the inverse of f\left(x\right)=\frac{-3}{x}+7 will be:

f^{-1}\:\left(x\right)=-\frac{3}{x-7}

Finding the domain of f^{-1}\:\left(x\right)=-\frac{3}{x-7}

As we know that domain is the set of the possible input values where the function is defined.

so the function domain must be: x7

Therefore,

\mathrm{Domain\:of\:}\:-\frac{3}{x-7}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x7\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:7\right)\cup \left(7,\:\infty \:\right)\end{bmatrix}

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