We have to find the inverse of the function f(x) = 2x + 3.
We can find the inverse function as:
[tex]\begin{gathered} f(f^{-1}(x))=x \\ 2f^{-1}(x)+3=x \\ 2f^{-1}(x)=x-3 \\ f^{-1}(x)=\frac{1}{2}x-\frac{3}{2} \end{gathered}[/tex]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]