Question

The function f(x) = 8x -4 is one-to-one.

(a) Find the inverse of f and check the answer.
(b) Find the domain and the range of f and f¹.
(c) Graph f, f¹, and y=x on the same coordinate axes.
x +4
8
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
(a) f¹(x) =
(b) Find the domain of f. Select the correct choice below and, if necessary, fill in the
answer box to complete your choice.
A. The domain is {xx
B. The domain is x.
OC. The domain is x².

Answer 1

(a) To find the reverse capability \(f^{-1}\), exchange \(x\) and \(y\) in the first capability and settle for \(y\):

\[ x = 8y - 4 \]

Addressing for \(y\), you get:

\[ f^{-1}(x) = \frac{x + 4}{8} \]

(b) The space of \(f\) is the arrangement of every single genuine number, and the reach is likewise the arrangement of every genuine number.

The space of \(f^{-1}\) is the arrangement of every single genuine number.

(c) To diagram \(f\), \(f^{-1}\), and \(y=x\) on similar direction tomahawks:

- \(f(x) = 8x - 4\) is a line with a slant of 8 and y-catch of - 4.

- \(f^{-1}(x) = \frac{x + 4}{8}\) is the reverse capability.

The space of \(f\) is all genuine numbers, so choice An is the right decision. Assuming that you have additional inquiries or need further explanation, go ahead and inquire!