Does an inverse function exist for the function f(x) = 2x + 3?

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frostylui

07.12.2021

Mathematics

Question:

What is the result of substituting for y in the bottom equation? y = x – 3 y = x2 + 2x – 4 A. (x – 3) = x2 B. y = (x – 3)2 + 2(x – 3) – 4 C. x – 3 = x2 + 2x – 4 D. y = x2 + 2x – 4 – (x – 3)

Option C: $x-3=x^{2}+2 x-4$ is the resulting equation

Explanation:

Given that y=x+3 and $y=x^{2}+2 x-4$

We need to determine the resulting equation by substituting the value of y in the equation $y=x^{2}+2 x-4$

Option A: $x-3=x^{2}$

Substituting the value of y in the second equation does not results the equation $x-3=x^{2}$ because the last two terms 2x-4 is missing.

Hence, Option A is not the correct answer.

Option B: $y=(x-3)^{2}+2(x-3)-4$

This is not the resulting expression because instead of substituting the value for y, it has been wrongly substituted for x.

Hence, Option B is not the correct answer.

Option C: $x-3=x^{2}+2 x-4$

This is the resulting expression because substituting y=x+3 in the second equation, we get, $x-3=x^{2}+2 x-4$

Hence, Option C is the correct answer.

Option D: $y=x^{2}+2 x-4-(x-3)$

This is not the resulting expression because instead of substituting the values for y, the value of y has been subtracted.

Hence, Option D is not the correct answer.

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