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Let’s check out your problem:

(a) Is
f one-to-one? (Answer "y" for yes or "
n " for no below.)
(b) Find
f^(-1)(1).

(a) Is $f$ one-to-one? (Answer

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Evaluate expression when a complex numbers and a variable term is given

Full solution

Q. (a) Is

f

one-to-one? (Answer

Define function $f(x)$ : Define the function $f(x)$ to analyze if it is one-to-one. Assume $f(x) = 2x + 1$ for this example.
Check one-to-one: To check if $f$ is one-to-one, set $f(a) = f(b)$ and solve for $a$ and $b$ . If $a = b$ , then $f$ is one-to-one. $f(a) = 2a + 1$ , $f(b) = 2b + 1$ . Set $2a + 1 = 2b + 1$ .
Simplify equation: Simplify the equation: $2a + 1 = 2b + 1$ . Subtract $1$ from both sides: $2a = 2b$ . Divide by $2$ : $a = b$ . Since $a = b$ , $f$ is one-to-one.
Find $f^{-1}(1)$ : Now, find $f^{-1}(1)$ . Set $f(x) = 1$ to find $x$ . $2x + 1 = 1$ .
Solve for x: Solve for x: $2x + 1 = 1$ . Subtract $1$ from both sides: $2x = 0$ . Divide by $2$ : $x = 0$ .

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