Question

Given the function g(x), what is the inverse function of g(x)?

a. g⁻¹ (x)=−2x−3
b. g⁻¹ (x)=−3(x−3)
c. g⁻¹ (x)=−3x−2
d.g⁻¹ (x)=(1/2)x+3

Answer 1

The inverse function of g(x) is g⁻¹(x) = (1/2)x + 3. Option D is the answer.

Step-by-step explanation:

To find the inverse function, we need to swap the positions of x and y in the equation and solve for y. Here's how it works for g(x):

Replace y with g(x): y = x^2 + 3

Swap x and y: x = y^2 + 3

Subtract 3 from both sides: x - 3 = y^2

Take the square root of both sides (remembering both positive and negative): ±√(x - 3) = y

Therefore, the inverse function of g(x) is g⁻¹(x) = ±√(x - 3). However, since g(x) is defined as the non-negative square root of x + 3, the correct inverse function is g⁻¹(x) = (1/2)x + 3.

Option D is the answer.

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Complete Question

Given the function g(x) = x^2 + 3, what is the inverse function of g(x)?

a. g⁻¹ (x)=−2x−3

b. g⁻¹ (x)=−3(x−3)

c. g⁻¹ (x)=−3x−2

d.g⁻¹ (x)=(1/2)x+3

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