Question

CWhich of the following is the inverse of F(x)=2x+3?COAa 4520-19B.0 с.OD.103765PREVIOUSG Search or type URI(3,0)(15,0)3YSUBMIT

Answer 1

We have to find the inverse of the function f(x) = 2x + 3.

We can find the inverse function as:

`\begin{gathered} f(f^(-1)(x))=x \\ 2f^(-1)(x)+3=x \\ 2f^(-1)(x)=x-3 \\ f^(-1)(x)=(1)/(2)x-(3)/(2) \end{gathered}`

From the options we can see that the slope has to be positive, so we can discard optiosn B and C.

Then, we can check option A:

- It has a y-intercept of -1.5, which is equal to -3/2.

- The x-intercept is (3,0), what indicates that it increases 0.5 units of y per unit increase in x. This corresponds to a slope of 0.5 or 1/2.

Then, as both characteristics match with the equation of the inverse, the right representation is option A.

Answer:

The inverse is f^-1(x) = 1/2*x - 3/2 [Option A]